Fourier Series/Absolute Value of x over Minus Pi to Pi

Theorem
For $x \in \left[ {- \pi \,.\,.\, \pi } \right]$:
 * $\displaystyle \left\vert x \right\vert = \frac \pi 2 - \frac 4 \pi \sum_{n \mathop = 1}^\infty \frac{\cos\left( {2n - 1} \right)x} {\left( {2n - 1} \right)^2}$