diff --git a/Lib/test/mathdata/math_testcases.txt b/Lib/test/mathdata/math_testcases.txt
index 4a38a3666bab208..b7a099ce92a3133 100644
--- a/Lib/test/mathdata/math_testcases.txt
+++ b/Lib/test/mathdata/math_testcases.txt
@@ -1311,9 +1311,9 @@ atan2pi20000 atan2pi inf 0 -> 0.5
 atan2pi20001 atan2pi -inf 0 -> -0.5
 atan2pi20002 atan2pi nan 0 -> nan
 
-atan2pi20000 atan2pi inf -0 -> 0.5
-atan2pi20001 atan2pi -inf -0 -> -0.5
-atan2pi20002 atan2pi nan -0 -> nan
+atan2pi21000 atan2pi inf -0 -> 0.5
+atan2pi21001 atan2pi -inf -0 -> -0.5
+atan2pi21002 atan2pi nan -0 -> nan
 
 atan2pi20003 atan2pi inf 1 -> 0.5
 atan2pi20004 atan2pi -inf 1 -> -0.5
@@ -1339,9 +1339,9 @@ atan2pi30000 atan2pi 0 inf -> 0.0
 atan2pi30001 atan2pi 0 -inf -> 1.0
 atan2pi30002 atan2pi 0 nan -> nan
 
-atan2pi30000 atan2pi -0 inf -> -0.0
-atan2pi30001 atan2pi -0 -inf -> -1.0
-atan2pi30002 atan2pi -0 nan -> nan
+atan2pi31000 atan2pi -0 inf -> -0.0
+atan2pi31001 atan2pi -0 -inf -> -1.0
+atan2pi31002 atan2pi -0 nan -> nan
 
 atan2pi30003 atan2pi 1 inf -> 0.0
 atan2pi30004 atan2pi 1 -inf -> 1.0
@@ -2247,3 +2247,8 @@ tanpi10275 tanpi -1.6591963470121216 -> 1.829921944286168
 tanpi20001 tanpi inf -> nan invalid
 tanpi20002 tanpi -inf -> nan invalid
 tanpi20003 tanpi nan -> nan
+
+tanpi30001 tanpi 0.5 -> inf divide-by-zero
+tanpi30002 tanpi -0.5 -> -inf divide-by-zero
+tanpi30003 tanpi 1.5 -> -inf divide-by-zero
+tanpi30004 tanpi -1.5 -> inf divide-by-zero
diff --git a/Lib/test/test_curses.py b/Lib/test/test_curses.py
index bbcf8d285a67743..7b059eb2e8e1414 100644
--- a/Lib/test/test_curses.py
+++ b/Lib/test/test_curses.py
@@ -3459,6 +3459,8 @@ def test_use_prescr_screen(self):
             with self.assertRaises(curses.error):
                 prescr.use(func)
         # Affecting the state before initscr() is what such a screen is for.
+        # use_env() is process-wide, not a property of this screen.
+        self.addCleanup(curses.use_env, True)
         prescr.use(lambda scr: curses.use_env(False))
         # The current screen is unchanged.
         screen.stdscr.refresh()
diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py
index a27996dd01c9d12..a1250c668223e7f 100644
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -2144,7 +2144,12 @@ def test_mtestfile(self):
         fail_fmt = "{}: {}{!r}: {}"
 
         failures = []
+        ids = set()
         for id, fn, args, expected, flags in parse_mtestfile(math_testcases):
+            if id in ids:
+                failures.append(f"Duplicate test id {id}")
+            ids.add(id)
+
             func = getattr(math, fn)
 
             if 'invalid' in flags or 'divide-by-zero' in flags:
diff --git a/Misc/NEWS.d/next/Core_and_Builtins/2026-09-04-22-00-00.gh-issue-156910.aBcD3f.rst b/Misc/NEWS.d/next/Core_and_Builtins/2026-09-04-22-00-00.gh-issue-156910.aBcD3f.rst
new file mode 100644
index 000000000000000..f717bbe5f16aa96
--- /dev/null
+++ b/Misc/NEWS.d/next/Core_and_Builtins/2026-09-04-22-00-00.gh-issue-156910.aBcD3f.rst
@@ -0,0 +1,3 @@
+Fix a deadlock in the :term:`free threaded <free threading>` build when
+setting ``__abstractmethods__`` on a type while another thread holds the
+type lock.
diff --git a/Misc/NEWS.d/next/Library/2026-08-17-17-39-41.gh-issue-155966.0YOADY.rst b/Misc/NEWS.d/next/Library/2026-08-17-17-39-41.gh-issue-155966.0YOADY.rst
new file mode 100644
index 000000000000000..2f556aef54a63a0
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2026-08-17-17-39-41.gh-issue-155966.0YOADY.rst
@@ -0,0 +1,2 @@
+:func:`math.tanpi` now raises :exc:`ValueError` for half-integer values
+(e.g., ``tanpi(1.5)``), as these are poles of the function.
diff --git a/Modules/mathmodule.c b/Modules/mathmodule.c
index 7988a77ab0abcca..16e7231214af2df 100644
--- a/Modules/mathmodule.c
+++ b/Modules/mathmodule.c
@@ -1343,10 +1343,10 @@ FUNC1D(tan, tan, 0,
 FUNC1(tanh, tanh, 0,
       "tanh($module, x, /)\n--\n\n"
       "Return the hyperbolic tangent of x.")
-FUNC1D(tanpi, m_tanpi, 1,
+FUNC1D(tanpi, m_tanpi, 0,
       "tanpi($module, x, /)\n--\n\n"
       "Return the tangent of x (measured in half-turns).",
-      "expected a finite input, got %s")
+      "expected a finite input not equal to a half-integer, got %s")
 
 /* Precision summation function as msum() by Raymond Hettinger in
    <https://code.activestate.com/recipes/393090-binary-floating-point-summation-accurate-to-full-p/>,
diff --git a/Objects/typeobject.c b/Objects/typeobject.c
index 572e302df8d80d5..30958310227af0e 100644
--- a/Objects/typeobject.c
+++ b/Objects/typeobject.c
@@ -1706,14 +1706,17 @@ type_set_abstractmethods(PyObject *tp, PyObject *value, void *Py_UNUSED(closure)
         return -1;
     }
 
+    pinned_mutexes_t pinned;
     BEGIN_TYPE_LOCK();
     _PyType_Modified_Unlocked(type);
+    type_lock_prevent_release(&pinned);
     types_stop_world();
     if (abstract)
         type_add_flags(type, Py_TPFLAGS_IS_ABSTRACT);
     else
         type_clear_flags(type, Py_TPFLAGS_IS_ABSTRACT);
     types_start_world();
+    type_lock_allow_release(&pinned);
     ASSERT_TYPE_LOCK_HELD();
     END_TYPE_LOCK();