Let $\vec{a}$, $\vec{b}$, $\vec{c}$ be three unit vectors such that $|\vec{a} + \vec{b} + \vec{c}| = 1$ and $\vec{a} \perp \vec{b}$. If $\vec{c}$ makes angles $\delta$ and $\beta$ with $\vec{a}$ and $\vec{b}$ respectively, then $\cos \delta + \cos \beta$ is equal to: