Using Parserval's identity in a Fourier series

Question

I have the function $$f(x)=\begin{cases}1, \space |x|\leq a \\ 0, \space a<|x|\leq 1/2\end{cases}$$ I have calculated the Fourier series of this even function: $$Sf(x)=2a+2\sum_{n=0}^\infty \frac{\sin(2\pi na)}{\pi n}\cos(2\pi nx)$$ Now I need to calculate $$\sum_{n=0}^\infty\frac{\sin^2(2\pi na)}{n^2}$$ How do I use Parserval's Identity to calculate this last sum? I have tried $$2a=\int_{-a}^a1^2=2a^2+\sum_{n=0}^\infty\frac{\sin^2(2\pi na)}{\pi^2 n^2}$$ And therefore $$(2a-2a^2)\pi^2=\sum_{n=0}^\infty\frac{\sin^2(2\pi na)}{n^2}$$ Is this correct? If not, what is the correct way to do it?