3 It is given that \(3 \cos \theta - 2 \sin \theta = R \cos ( \theta + \alpha )\), where \(R > 0\) and \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\).
- Find the value of \(R\).
- Show that \(\alpha \approx 33.7 ^ { \circ }\).
- Hence write down the maximum value of \(3 \cos \theta - 2 \sin \theta\) and find a positive value of \(\theta\) at which this maximum value occurs.