Question 5 - A-Level Maths

Show that the equation $$\frac { \cos \theta - 4 } { \sin \theta } - \frac { 4 \sin \theta } { 5 \cos \theta - 2 } = 0$$ may be expressed as $9 \cos ^ { 2 } \theta - 22 \cos \theta + 4 = 0$.
Hence solve the equation $$\frac { \cos \theta - 4 } { \sin \theta } - \frac { 4 \sin \theta } { 5 \cos \theta - 2 } = 0$$ for $0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }$.