As the question says, use a Fourier Sine series. Here
$\displaystyle
f(x) = \frac{\pi-x}{2} = \sum_{n=1}^{\infty} a_n \sin nx
$
where $\displaystyle a_n = \frac{2}{\pi} \int_0^{\pi} f(x) \sin nx\,dx = \frac{1}{n }$
so
$\displaystyle
\frac{\pi-x}{2} = \sum_{n=1}^{\infty} \frac{\sin nx}{n}
$
Now sub. in $\displaystyle x = \frac{\pi}{2}$