$\large \dfrac {2x}{\sqrt 3} = y \sqrt 2 = \dfrac {2z}{\sqrt {2-\sqrt 3}}$

Consider a triangle with side lengths $x$, $y$ and $z$ satisfying the equation above. If the longest side has length 303, then the circumradius of this triangle can be expressed as $a \sqrt b$, where $a$ and $b$ are positive integers with $b$ square-free. Find $a+b$.

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