Proving $\frac{\sin n\theta}{\sin\theta}= 2^{n-1}\prod_{k=1}^{n-1}\left(\cos\theta-\cos\frac{\pi k}n\right)$
How one can prove $\prod_{k=1}^{n-1} (\cos\theta-\cos(k\pi/n)) = 2^{1-n}\sin(n\theta)\csc\theta$?