# Finding Sum for Infinite Series

Normally when I keep try multiple ways to solve a problem, I get an idea of where to start, and eventually can solve it. But it hasn't been the way for this question and I've been stuck for hours.

I'm trying to determine the sum of the series $\sum_{n=1}^\infty{\frac{1}{2^n}\tan(\frac{x}{2^n})}$;

Yet, this isn't a geometric series, a telescoping series, and when I tried to expand it in the Fourier series in an attempt to reduce some of the factors, that didn't work either.