2. (a) Find all values of \(\theta\) in the range \(0 ^ { \circ } < \theta < 360 ^ { \circ }\) satisfying $$3 \cot \theta + 4 \operatorname { cosec } ^ { 2 } \theta = 5 .$$ (b) By writing \(24 \cos x - 7 \sin x\) in the form \(R \cos ( x + \alpha )\), where \(R\) and \(\alpha\) are constants with \(R > 0\) and \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\), solve the equation $$24 \cos x - 7 \sin x = 16$$ for values of \(x\) between \(0 ^ { \circ }\) and \(360 ^ { \circ }\).