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

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