We have a quadrilateral \(DEFG\) inscribed in a semicircle with center \(H\) such that point \(G\) is on the diameter \(AB\) of the semicircle and at the same time line \(FG\) is perpendicular to \(AB\). Suppose that \(2FG=DE=EF\). Find the measure of \(\angle GDE\) in degrees.
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Point \(D\) coincides with either Point \(A\) or \(B\)