Show that the equation \(2 \cos ^ { 2 } \theta + 7 \sin \theta = 5\) may be written in the form
$$2 \sin ^ { 2 } \theta - 7 \sin \theta + 3 = 0$$
By factorising this quadratic equation, solve the equation for values of \(\theta\) between \(0 ^ { \circ }\) and \(180 ^ { \circ }\).
Section B (36 marks)