Find All Solutions of the Following Equation in the Interval $2 \cos ^ { 3 } x = 2 \cos x$

Multiple Choice

Find all solutions of the following equation in the interval [0,2π) .​ $2 \cos ^ { 3 } x = 2 \cos x$ ​

A) $0 , \frac { \pi } { 2 } , 2 \pi , \frac { 3 \pi } { 4 }$
B) ​ $0 , \frac { \pi } { 2 } , 3 \pi , \frac { 3 \pi } { 2 }$
C) ​ $0 , \frac { \pi } { 3 } , \pi , \frac { 2 \pi } { 3 }$
D) ​ $0 , \frac { \pi } { 4 } , \pi , \frac { 2 \pi } { 3 }$
E) ​ $0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 }$