Geometric Sequence of Trig Expressions

For some angles $\theta$, the three numbers $2-2\cos\theta$, $1+\sin\theta$, $2+2\cos \theta$ form a geometric sequence in that order. Determine the sum of all distinct values of $\cos^2\theta$. The answer is in the form $\frac{\alpha}{\beta}$ for coprime integers $\alpha$ and $\beta$. Input the answer as the sum $\alpha +\beta$.