9. In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
Given that \(\cos 2 \theta - \sin 3 \theta \neq 0\)
- prove that
$$\frac { \cos ^ { 2 } \theta } { \cos 2 \theta - \sin 3 \theta } \equiv \frac { 1 + \sin \theta } { 1 - 2 \sin \theta - 4 \sin ^ { 2 } \theta }$$
- Hence solve, for \(0 < \theta \leqslant 360 ^ { \circ }\)
$$\frac { \cos ^ { 2 } \theta } { \cos 2 \theta - \sin 3 \theta } = 2 \operatorname { cosec } \theta$$
Give your answers to one decimal place.
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