If cos a + cos b = 3 2 and sin a + sinb 1 2 and q is the the arithmetic mean of a and b , then sin 2q + cos 2q is equal to :

If $\cos \alpha+\cos \beta=\frac{3}{2}$ and $\sin \alpha+\sin \beta \frac{1}{2}$ and $\theta$ is the the arithmetic mean of $\alpha$ and $\beta$, then $\sin 2 \theta+\cos 2 \theta$ is equal to :