Compute $\sum_{n=1}^\infty \frac{1}{n^2}$ and $\sum_{n\geq 1,\ k\rm\ odd}\frac{1}{n^2}$ using fourier series.

Question

Let $f(x)=|x|$ on $[-\pi,\pi]$. A compute it's fourier coefficient, which are $c_n=\frac{-1+(-1)^n}{\pi n^2}$ if $n\neq 0$ and $c_0 = \frac{\pi}{2}$. Then, I could compute $\sum_{k\geq 1,k\rm\ odd}\frac{1}{n^2}$, but how can I deduce $\sum_{k=1}^\infty \frac{1}{n^2}$ ?