Eliminate $\theta$ from $\lambda \cos2\theta=\cos(\theta + \alpha)$ and $\lambda\sin2\theta=2\sin(\theta + \alpha)$
My approach:
Dividing the RHS and LHS of both equations by $\lambda$, then squaring and adding them, we get, $$\frac{\cos^2(\theta+\alpha)}{\lambda^2}+\frac{4\sin^2(\theta+\alpha)}{\lambda^2}=\cos^22\theta + \sin^22\theta=1$$ $$\Rightarrow \sin^2(\theta+\alpha)=\frac{\lambda^2-1}{3}$$ I am unable to proceed.