solved thanks
You may want to open up the sum you got: it's exactly the same as in the question, so you already have (1)
As for (2): according to what you wrote: $\displaystyle 0=f(0)=\frac{\pi^2}{3}+4\sum\limits^\infty_{n=1}\f rac{(-1)^n}{n^2}\Longrightarrow \sum\limits^\infty_{n=1}\frac{(-1)^{n-1}}{n^2}=\frac{\pi^2}{12}$.
Likewise: $\displaystyle \pi^2=f(\pi)=\frac{\pi^2}{3}+4\sum\limits^\infty_{ n=1}\frac{1}{n^2}\Longrightarrow$ ....get the sum
Tonio