- (a) Solve, for \(- 180 ^ { \circ } \leqslant x < 180 ^ { \circ }\), the equation
$$3 \sin ^ { 2 } x + \sin x + 8 = 9 \cos ^ { 2 } x$$
giving your answers to 2 decimal places.
(b) Hence find the smallest positive solution of the equation
$$3 \sin ^ { 2 } \left( 2 \theta - 30 ^ { \circ } \right) + \sin \left( 2 \theta - 30 ^ { \circ } \right) + 8 = 9 \cos ^ { 2 } \left( 2 \theta - 30 ^ { \circ } \right)$$
giving your answer to 2 decimal places.