By first expanding \(\cos \left( x - 60 ^ { \circ } \right)\), show that the expression
$$2 \cos \left( x - 60 ^ { \circ } \right) + \cos x$$
can be written in the form \(R \cos ( x - \alpha )\), where \(R > 0\) and \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\). Give the exact value of \(R\) and the value of \(\alpha\) correct to 2 decimal places.
Hence find the value of \(x\) in the interval \(0 ^ { \circ } < x < 360 ^ { \circ }\) for which \(2 \cos \left( x - 60 ^ { \circ } \right) + \cos x\) takes its least possible value.