Show that \(\cos \theta = \frac { 1 } { 2 }\) is one solution of the equation
$$6 \sin ^ { 2 } \theta + 5 \cos \theta = 7$$
6
(ii) Find all the values of \(\theta\) that solve the equation
$$6 \sin ^ { 2 } \theta + 5 \cos \theta = 7$$
for \(0 ^ { \circ } \leq \theta \leq 360 ^ { \circ }\)
Give your answers to the nearest degree.
6
Hence, find all the solutions of the equation
$$6 \sin ^ { 2 } 2 \theta + 5 \cos 2 \theta = 7$$
for \(0 ^ { \circ } \leq \theta \leq 360 ^ { \circ }\)
Give your answers to the nearest degree.