7. (i) (a) Express \(( 12 \cos \theta - 5 \sin \theta )\) in the form \(R \cos ( \theta + \alpha )\), where \(R > 0\) and \(0 < \alpha < 90 ^ { \circ }\).
(b) Hence solve the equation $$12 \cos \theta - 5 \sin \theta = 4$$ for \(0 < \theta < 90 ^ { \circ }\), giving your answer to 1 decimal place.
(ii) Solve $$8 \cot \theta - 3 \tan \theta = 2$$ for \(0 < \theta < 90 ^ { \circ }\), giving your answer to 1 decimal place.