Problems regarding Fourier series

Question

Given that $f(x) = x^2$, I got that the Fourier series is $$ x^2 = \dfrac{\pi^2}{3} + \sum\limits_{n=1}^{\infty} (-1)^n \cdot 4 \cdot \dfrac{\cos(nx)}{n^2} $$ for $x \in [-\pi, \pi]$. From the above series, how can I find $\sum\limits_{n=1}^{\infty} \frac{1}{(2n-1)^2}$?

Answer 1

Hint:

Consider $x = \pi$ and then $x = 0$. Then, add the two results and see what you get.