If $(\cos\alpha+i\sin\alpha)(\cos2\alpha+i\sin2\alpha)....(\cos n\alpha+i \sin n\alpha)$ = 1, then $\alpha$ = ?

Question

$\begin{array}{1 1}(A)4n \pi \\ (B) \large\frac{2n\pi}{n(n+1)} \\ (C) \large\frac{4n \pi}{n(n+1)} \\(D) \large\frac{n \pi}{n(n+1)} \end{array}$