I was given an exercise:
Calculate 1+$\sum_{k=1}^{k=n}\frac{\sin(kx)}{\sin^{k}(x)}$
I recognize $\sin(kx)=Im(cis(kx))=Im(cis^{k}(x))$ and $\sin^{k}(x)=(Im(cis(x)))^{k}$ but I do not know how to proceed .
I would appreciate any help or hint on how to get started, I guess that is should be related to geometric series, but I didn't manage to get to any geometric series.