Express theta - sqrt(3) theta in the form R (theta - lambda), and find the value of R and lambda.

3. (ii)

Step 1: Express $\sin \theta - \sqrt{3} \cos \theta$ in the form $R \sin(\theta - \lambda)$.
We compare $\sin \theta - \sqrt{3} \cos \theta$ with the expansion of $R \sin(\theta - \lambda)$:

$$R \sin(\theta - \lambda) = R(\sin \theta \cos \lambda - \cos \theta \sin \lambda) = (R \cos \lambda) \sin \theta - (R \sin \lambda) \cos \theta$$

Equating the coefficients of $\sin \theta$ and $\cos \theta$:

$$$$