Express \(4 \cos \theta - 2 \sin \theta\) in the form \(R \cos ( \theta + \alpha )\), where \(R > 0\) and \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\).
Hence
(a) solve the equation \(4 \cos \theta - 2 \sin \theta = 3\) for \(0 ^ { \circ } < \theta < 360 ^ { \circ }\),
(b) determine the greatest and least values of
$$25 - ( 4 \cos \theta - 2 \sin \theta ) ^ { 2 }$$
as \(\theta\) varies, and, in each case, find the smallest positive value of \(\theta\) for which that value occurs.