If $$\theta \in R$$ and $${{1 - i\cos \theta } \over {1 + 2i\cos \theta }}$$ is real number, then $$\theta $$ will be (when I : Set of integers)

The complex number z satisfying the equation | z $$-$$ 1 | = | z + 1 | = 1 is

If z = sin$$\theta$$ $$-$$ icos$$\theta$$, then for any integer n,