Solve the Equation in the Interval [0°, 360°) $$2 \cos ^ { 3 } \theta = \cos \theta$$

Solve the equation in the interval [0°, 360°) . Give solutions to the nearest tenth, if necessary.
- $$2 \cos ^ { 3 } \theta = \cos \theta$$

A) $\left\{ 90 ^ { \circ } , 270 ^ { \circ } \right\}$
B) $\left\{ 45 ^ { \circ } , 90 ^ { \circ } , 135 ^ { \circ } , 225 ^ { \circ } , 270 ^ { \circ } , 315 ^ { \circ } \right\}$
C) $\left\{ 45 ^ { \circ } , 135 ^ { \circ } , 225 ^ { \circ } , 315 ^ { \circ } \right\}$
D) $\varnothing$