Find All Solutions of the Following Equation in the Interval $[ 0,2 \pi )$

Multiple Choice

Find all solutions of the following equation in the interval $[ 0,2 \pi )$ .
$$\csc ^ { 2 } x = \cot x + 1$$

A) $x = \frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 4 \pi } { 3 }$
B) $x = \frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$
C) $x = 0 , \frac { \pi } { 2 } , \pi , \frac { 3 \pi } { 2 }$
D) $x = \frac { \pi } { 4 } , \frac { \pi } { 2 } , \frac { 5 \pi } { 4 } , \frac { 3 \pi } { 2 }$
E) $x = \frac { \pi } { 4 } , \frac { 4 \pi } { 3 } , \frac { 11 \pi } { 6 }$