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sage: a.simplify_full()
-(sqrt(sqrt(3) - 2)*sqrt(2) + I*sqrt(3) - I)/(sqrt(sqrt(3) - 2)*(sqrt(2)*sqrt(3) - sqrt(2)))
See Trac 12737 for what the problem likely is for this. In my view, this is buyer beware of simplification (!) but at any rate to be fair I will link this question there as well. For now:
sage: a.simplify_trig()
-(sqrt(-2*sqrt(3) + 4) - sqrt(3) + 1)/(sqrt(-2*sqrt(3) + 4)*(sqrt(3) - 1))
sage: a.simplify_trig().n()
-4.14340873563388e-16
