Question 4 - A-Level Maths

Express $3 \sin \theta + 2 \cos \theta$ in the form $R \sin ( \theta + \alpha )$, where $R > 0$ and $0 ^ { \circ } < \alpha < 90 ^ { \circ }$, stating the exact value of $R$ and giving the value of $\alpha$ correct to 2 decimal places.
Hence solve the equation $$3 \sin \theta + 2 \cos \theta = 1$$ for $0 ^ { \circ } < \theta < 180 ^ { \circ }$.