In a square \(ABCD\), \(E\) and \(F\) are the midpoints of sides \(AB\) and \(AD\), respectively. A point \(G\) is taken on segment \(CF\) in such a way that \(2CG=3FG\).

If the side of the square is \(2\), then what is the area of \(\triangle{BEG}\)?

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