Question

Please help, let: \[\frac{1}{2}+\sum_{k=1}^{n}\cos(kx)=\frac{sin(xn+\frac{x}{2})}{2sin(\frac{x}{2})}\]
Calculate: \[\frac{1}{\Pi}\int\limits_{-\pi}^{\pi}\frac{sin(xn+\frac{x}{2})}{2sin(\frac{x}{2})}dx\]