Question 6 - A-Level Maths

Express $3 \cos x + 2 \cos \left( x - 60 ^ { \circ } \right)$ in the form $R \cos ( x - \alpha )$, where $R > 0$ and $0 ^ { \circ } < \alpha < 90 ^ { \circ }$. State the exact value of $R$ and give $\alpha$ correct to 2 decimal places.
Hence solve the equation $$3 \cos 2 \theta + 2 \cos \left( 2 \theta - 60 ^ { \circ } \right) = 2.5$$ for $0 ^ { \circ } < \theta < 180 ^ { \circ }$.