## How do I show that $n=2$ is the only integer satisfy :$\cos^n\theta+ \sin^n\theta=1$ for all $\theta$ real or complex February 6

It is well known that :$\cos²\theta+ \sin²\theta=1$ for all $\theta$ real or complex ,I would like to ask about the general equality :$\cos^n\theta+ \sin^n\theta=1$ if there is others values of the positive integer $n$ than $n=2$ for which : $$\cos^n