Let $\vec{a}$, $\vec{b}$, and $\vec{c}$ be vectors of equal magnitude such that the angle between $\vec{a}$ and $\vec{b}$ is $\alpha$, between $\vec{b}$ and $\vec{c}$ is $\beta$, and between $\vec{c}$ and $\vec{a}$ is $\gamma$. What is the minimum value of $\cos \alpha + \cos \beta + \cos \gamma$?