Let $\vec { a }$ and $\vec { b }$ be two unit vectors such that $\vec { a } \cdot \vec { b } = 0$. For some $x , y \in \mathbb { R }$, let $\vec { c } = x \vec { a } + y \vec { b } + ( \vec { a } \times \vec { b } )$. If $| \vec { c } | = 2$ and the vector $\vec { c }$ is inclined at the same angle $\alpha$ to both $\vec { a }$ and $\vec { b }$, then the value of $8 \cos ^ { 2 } \alpha$ is $\_\_\_\_$.