By using a suitable trigonometric identity, show that the equation
$$\sin \theta \tan \theta = 4 \cos \theta$$
can be written as
$$\tan ^ { 2 } \theta = 4$$
4
(ii) Hence solve the equation
$$\sin \theta \tan \theta = 4 \cos \theta$$
where \(0 ^ { \circ } < \theta < 360 ^ { \circ }\)
Give your answers to the nearest degree.
4
Deduce all solutions of the equation
$$\sin 3 \alpha \tan 3 \alpha = 4 \cos 3 \alpha$$
where \(0 ^ { \circ } < \alpha < 180 ^ { \circ }\)
Give your answers to the nearest degree.