Express \(8 \cos \theta - 15 \sin \theta\) in the form \(R \cos ( \theta + \alpha )\), where \(R > 0\) and \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\), stating the exact value of \(R\) and giving the value of \(\alpha\) correct to 2 decimal places.
Hence solve the equation
$$8 \cos 2 x - 15 \sin 2 x = 4$$
for \(0 ^ { \circ } < x < 180 ^ { \circ }\).