Find the Solutions of the Equation That Are in the Interval

Multiple Choice

Find the solutions of the equation that are in the interval $[ 0,2 \pi ) .$ $\cot ^ { 2 } u \cos u = \cos u$

A) $\frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }$
B) $0 , \pi , \frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$
C) $0 , \pi , \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }$
D) $\frac { \pi } { 2 } , \frac { 3 \pi } { 2 } , \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }$
E) no solution