Given that \(\frac { \sin \theta - \cos \theta } { \cos \theta } = 4\), prove that \(\tan \theta = 5\).
Use an appropriate identity to show that the equation
$$2 \cos ^ { 2 } x - \sin x = 1$$
can be written as
$$2 \sin ^ { 2 } x + \sin x - 1 = 0$$
Hence solve the equation
$$2 \cos ^ { 2 } x - \sin x = 1$$
giving all solutions in the interval \(0 ^ { \circ } \leqslant x \leqslant 360 ^ { \circ }\).