Sejam $\alpha ,\beta ,\gamma \in \mathbb{R}$ tais que $\alpha +\beta +\gamma =-3\pi$, $\mathrm{sen}\alpha +\mathrm{sen}\beta +\mathrm{sen}\gamma =\frac{1}{2}$ e $\cos \alpha +\cos \beta +\cos \gamma =-\frac{1}{2}$. Determine o valor de $\cos {\alpha }^2+\cos {\beta }^2+\cos {\gamma }^2$