Question 6 - A-Level Maths

Show that the equation $\cot ^ { 2 } \theta + 2 \cos 2 \theta = 4$ can be written in the form $$4 \sin ^ { 4 } \theta + 3 \sin ^ { 2 } \theta - 1 = 0$$
Hence solve the equation $\cot ^ { 2 } \theta + 2 \cos 2 \theta = 4$, for $0 ^ { \circ } < \theta < 360 ^ { \circ }$.