If cos α+ cos β=3/2 and sin α+ sin β=1/2 and θ is the arithmetic mean of α and β, then sin 2 θ+ cos 2 θ is equal to:

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