By first expanding \(2 \sin \left( x - 30 ^ { \circ } \right)\), express \(2 \sin \left( x - 30 ^ { \circ } \right) - \cos x\) in the form \(R \sin ( x - \alpha )\), 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. [5]
Hence solve the equation
$$2 \sin \left( x - 30 ^ { \circ } \right) - \cos x = 1$$
for \(0 ^ { \circ } < x < 180 ^ { \circ }\).