Horrible Hexagons 2

Geometry Level 3

The diagram above shows a regular hexagon with side length \(2\) and two equilateral triangles inscribed in it.

The area of the shaded region can be written as \(\large \frac { a\sqrt { 3 } }{ b } \), where \(a\) and \(b\) are coprime integers. Find \(ab\).

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