trigonometry - How to evaluate $sum_{k=1} ^{n-1} frac{sin (ktheta)}{sin theta}$

How to evaluate $$\sum_{k=1} ^{n-1} \frac{\sin (k\theta)}{\sin \theta}$$

Any help ? I tried to use difference method. But I'm not getting there.

Answer

HINT:

Use the Prosthaphaeresis Formula,

$$\cos((k-1)\theta)-\cos((k+1)\theta)=2\sin(k\theta)\sin(\theta)$$

and then sum the resulting telescoping series.