Welcome 2015!!!!

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.