Sum of Reciprocals of Squares of Odd Integers/Proof 5

Proof
By Fourier Series of Modulus of x, for $x \in \left[ {- \pi \,.\,.\, \pi } \right]$:


 * $\displaystyle \left\vert x \right\vert = \frac \pi 2 - \frac 4 \pi \sum_{n \mathop = 1}^\infty \frac{\cos \left( {2n - 1} \right) x} {\left( {2 n - 1} \right)^2}$

Setting $x = \pi$: