Inscribed Semicircle Riddle

Geometry Level 2

As shown in the diagram, triangle \(ABC\) inscribes a semi-circle such that \(AB\) and \(AC\) are tangents at points \(D\) and \(E,\) respectively.

\(GH\) is the diameter of the semi-circle, and point \(F\) is the intersection of \(DH\) and \(EG.\)

If the 2 angles highlighted in blue are equal, find that angle in degrees.

\(\)
Note: The diagram is not drawn to scale.

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