Question 2 - A-Level Maths

Show that the equation \(4 \sin ^ { 4 } \theta + 5 = 7 \cos ^ { 2 } \theta\) may be written in the form \(4 x ^ { 2 } + 7 x - 2 = 0\), where \(x = \sin ^ { 2 } \theta\).
Hence solve the equation \(4 \sin ^ { 4 } \theta + 5 = 7 \cos ^ { 2 } \theta\), for \(0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }\).