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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