Find All Solutions of the Equation $$( \cos \theta - 1 ) ( \sin \theta + 1 ) = 0$$

Multiple Choice

Find all solutions of the equation. $$( \cos \theta - 1 ) ( \sin \theta + 1 ) = 0$$

A) $2 \pi$ and $- \frac { \pi } { 2 } + 2 \pi n$ for every integer n.
B) $2 \pi$ and $\pi + 2 \pi n$ for every integer n.
C) $\pi + 2 \pi n$ and $\frac { \pi } { 2 } + 2 \pi n$ for every integer n.
D) $\frac { \mathrm { mn } } { 2 }$ for every integer n.
E) $\pi + 2 \pi n$ and $- \frac { \pi } { 2 } + \pi n$ for every integer n.