In parallelogram \(ABCD\) shown above, \(E\) is the midpoint of \(BC\), \(F\) is the midpoint of \(CD\). \(G\) is a point on \(EF\) such that ratio \( EG : GF \) equal \(1 : 2 \). If the area of this parallelogram is 776, find Area of triangle \(AEG\).

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