Response of a seismic array

Question

I need to prove: $$\sum_{r=0}^{n-1}\sin(\omega t-r\gamma)=\dfrac{\sin(\frac{1}{2}n\gamma)}{\sin(\frac{1}{2}\gamma)}\sin[\omega t-\dfrac{1}{2}(n-1)\gamma]$$

Hint: $\cos x-i\sin x=e^{-ix}$