Show that the equation \(15 \cos ^ { 2 } \theta ^ { \circ } = 13 + \sin \theta ^ { \circ }\) may be written as a quadratic equation in \(\sin \theta ^ { \circ }\).
Hence solve the equation, giving all values of \(\theta\) such that \(0 \leqslant \theta \leqslant 360\).