Algebra and Geometry Don't Fit Well!

Geometry Level 5

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

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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