Show that the equation \(\sin ^ { 2 } \theta + 3 \sin \theta \cos \theta = 4 \cos ^ { 2 } \theta\) can be written as a quadratic equation in \(\tan \theta\).
Hence, or otherwise, solve the equation in part (i) for \(0 ^ { \circ } \leqslant \theta \leqslant 180 ^ { \circ }\).