8. In this question the angle \(\theta\) is measured in degrees throughout.
- Show that the equation
$$\frac { 5 + \sin \theta } { 3 \cos \theta } = 2 \cos \theta , \quad \theta \neq ( 2 n + 1 ) 90 ^ { \circ } , \quad n \in \mathbb { Z }$$
may be rewritten as
$$6 \sin ^ { 2 } \theta + \sin \theta - 1 = 0$$
- Hence solve, for \(- 90 ^ { \circ } < \theta < 90 ^ { \circ }\), the equation
$$\frac { 5 + \sin \theta } { 3 \cos \theta } = 2 \cos \theta$$
Give your answers to one decimal place, where appropriate.