I'm not asking the solution, but rather the main idea of how to solve the part 2:

1)Find the Fourier development of $\displaystyle f(t)=|t|$ with $\displaystyle -\pi \leq t \leq \pi$.

2)Show using the previous result that $\displaystyle \sum _{k=0}^{\infty} \frac{1}{(2k+1)^2}=\frac{\pi ^2}{8}$.

Attempt: Is it just by using Parseval's theorem?