JEE Math Practice Question

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 the same angle $\alpha$ to both $\vec{a}$ and $\vec{b}$, then what is the value of $8 \cos ^{2} \alpha$?