Trapped inside a trapezium

Geometry Level 3

A trapezium \(ABCD\) ( with \(AB || CD\) ) is inscribed inside a circle of centre \(O\) and its diagonals \(AC\) and \(BD\) intersect each other at \(M \). If \(OM = 2\) and \(\angle AMB = 60 ^\circ\), then find the difference between the parallel sides.

If your answer is \(p\sqrt q\), where \(p \) and \(q\) are positive integers with \(q\) square-free, submit \(p+q\).

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