Updates:
        Status: Valid
        Labels: -Priority-Low Priority-Medium Simplify

Comment #1 on issue 3896 by [email protected]: sum of three-phase cos^2 or cos^4 do not simplify to 3/2 and 9/8, respectively
http://code.google.com/p/sympy/issues/detail?id=3896

The k = 2 case works in master:

In [22]: k = 2

In [23]: simplify(cos(theta)**k + cos(theta+2*pi/3)**k + cos(theta+4*pi/3)**k)
Out[23]: 3/2

k = 4 does not, though. trigsimp implements the algorithm from "Automated and readable simplification of trigonometric expressions" by Fu, et. al.

It is possible to do this simplification in any case, though. Just explicitly call expand_trig on it first. This will expand the sines and cosines using the sum formulas, and the rest is just simplification using sin(theta)**2 + cos(theta)**2 = 1, which trigsimp is quite good at.

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