The real solution of the equation below can be expressed as $x=z+z^{*}$, where $z$ is a complex number, with $|z|=1$. If $\arg{z}=\frac{a}{b}\pi$, where $a$ and $b$ are co-prime, find $b-a$.
$x=\sqrt{2+\sqrt{2-\sqrt{2+x}}}$

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