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

Question

$\begin{array}{1 1} \frac{3}{5} \\ \frac{4}{5} \\ \frac{7}{5} \\ \frac{8}{5} \end{array} $