Riemann Zeta Function at Even Integers/Lemma

Lemma
Let $x \in \R$ be such that $\left\lvert{x}\right\rvert < 1$.

Then:
 * $\displaystyle \pi x \cot {\pi x} = 1 - 2 \sum_{n \mathop = 1}^\infty \zeta \left({2 n}\right) x^{2 n}$

where $\zeta$ denotes the Riemann zeta function.