Welcome 2015!!!!

Algebra Level pending

If \(1/z+z=2\cos { \theta } \) then, The value of the expression \(\frac { 1 }{ { z }^{ 2015 } } +{ z }^{ 2015 } \) can be expressed in the form \(k\cos { n\theta }\) where \(k\) and \(n\) are integers, what is the value of \(n+k\) ?

P.S. This problem is not original. I just feel like this needs to be shared here.

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