Three Cosines in Concert

The value of $$\cos^2 10^\circ+\cos^2 50^\circ+\cos^2 70^\circ$$can be expressed in the form $\frac{\alpha}{\beta}$ where $\alpha$ and $\beta$ are positive integers, and $\gcd(\alpha,\beta) =1$. Find the value of $\alpha+\beta$.