Comment #1 on issue 3609 by [email protected]: KeyError in trigsimp (cot(x).equals(tan(x)))
http://code.google.com/p/sympy/issues/detail?id=3609

The obvious fix highlights some other problem that I can track down later unless someone else gets to it first:

@@ -1735,10 +1742,11 @@ def __trigsimp(expr, deep=False):
                 if m[a_t] == 0 or \
                         -m[a_t] in m[c].args or m[a_t] + m[c] == 0:
                     break
-                if d in m.keys() and m[a_t]*m[d] + m[c] == 0:
+                if d in m and m[a_t]*m[d] + m[c] == 0:
                     break
                 expr = result.subs(m)
                 m = expr.match(pattern)
+                m.setdefault(c, S.Zero)

With that change the OP expression now hangs and some pattern is generating a nan during trigsimp.

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