7 Let \(\mathrm { f } ( x ) = 8 x ^ { 3 } + 54 x ^ { 2 } - 17 x - 21\).
- Show that \(x + 7\) is a factor of \(\mathrm { f } ( x )\).
- Find the quotient when \(\mathrm { f } ( x )\) is divided by \(x + 7\).
- Hence solve the equation
$$8 \cos ^ { 3 } \theta + 54 \cos ^ { 2 } \theta - 17 \cos \theta - 21 = 0$$
for \(0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }\).