summation

\\\texttt{just an attempt } \\ \\ S_1 = Im(e^{i\theta}+e^{i2\theta}r+e^{i3\theta}r^2+....e^{ik\theta}.r^{k-1}) =\sin(\theta)+\sin(2\theta)r+...........\sin(k\theta)r^{k-1} \\ \\ \\\texttt{now we have the G.P} \\ \\ S_2=\frac{\cos\theta}{1}+\frac{\cos^2\theta}{r}+...............+\frac{\cos^k\theta}{r^{k-1}} \\ \\ \\\texttt{coefficient of } \ x^0 \\\texttt{in the expansion of }S_1.S_2\\\texttt{must give the answer }