6 In this question you must show detailed reasoning.
The cubic polynomial \(\mathrm { f } ( x )\) is defined by \(\mathrm { f } ( x ) = 4 x ^ { 3 } + 4 x ^ { 2 } + 7 x - 5\).
- Show that \(( 2 x - 1 )\) is a factor of \(\mathrm { f } ( x )\).
- Hence solve the equation \(4 \sin ^ { 3 } \theta + 4 \sin ^ { 2 } \theta + 7 \sin \theta - 5 = 0\) for \(0 ^ { \circ } \leq \theta \leq 360 ^ { \circ }\).