Prove that $$\sin(x) +\sin(3x)+\cdots + \sin((2n-1)x) = \frac{\sin^2(nx)}{\sin(n)}$$ where $n=1,2,3,\cdots$
This was done by my prof in lecture, but he went pretty quickly and I didn't really grasp what he was saying. Can anyone explain the proof for this problem?