diff -r eb0370d4686c Lib/random.py
--- a/Lib/random.py	Thu Feb 07 16:26:55 2013 +0200
+++ b/Lib/random.py	Sun Feb 10 12:33:15 2013 +0000
@@ -450,9 +450,9 @@
 
         u3 = random()
         if u3 > 0.5:
-            theta = (mu % TWOPI) + _acos(f)
+            theta = (mu + _acos(f)) % TWOPI
         else:
-            theta = (mu % TWOPI) - _acos(f)
+            theta = (mu - _acos(f)) % TWOPI
 
         return theta
 
diff -r eb0370d4686c Lib/test/test_random.py
--- a/Lib/test/test_random.py	Thu Feb 07 16:26:55 2013 +0200
+++ b/Lib/test/test_random.py	Sun Feb 10 12:33:15 2013 +0000
@@ -512,6 +512,18 @@
             self.assertAlmostEqual(s1/N, mu, places=2)
             self.assertAlmostEqual(s2/(N-1), sigmasqrd, places=2)
 
+    def test_von_mises_range(self):
+        # Issue 17149: von mises variates were not consistently in the
+        # range [0, 2*PI].
+        g = random.Random()
+        N = 100
+        for mu in 0.0, 0.1, 3.1, 6.2:
+            for kappa in 0.0, 2.3, 500.0:
+                samples = [g.vonmisesvariate(mu, kappa) for _ in range(N)]
+                self.assertTrue(
+                    all(0 <= sample <= random.TWOPI for sample in samples)
+                )
+
 class TestModule(unittest.TestCase):
     def testMagicConstants(self):
         self.assertAlmostEqual(random.NV_MAGICCONST, 1.71552776992141)