The general value of the real angle \(\theta\), which satisfies the equation, \((\cos \theta+i \sin \theta)(\cos 2 \theta+i \sin 2 \theta) \ldots \ldots .\) \((\cos n \theta+i \sin n \theta)=1\) is given by, (assuming \(k\) is an integer)
(A) \(\frac{2 k \pi}{n+2}\)
(B) \(\frac{4 k \pi}{n(n+1)}\)
(C) \(\frac{4 k \pi}{n+1}\)
(D) \(\frac{6 k \pi}{n(n+1)}\)