In the right triangle ABC, with a right angle at B, points D, E, and F are located at the midpoints of the sides AC, AB, and BC, respectively. Then, the equilateral triangles AEG and CFH are constructed, as shown in the figure. Calculate the measure of angle DHG.
In right-angled embrace,
Midpoints form triangles' grace,
Angles whisper tales,
Seeking DHG's hidden place,
Geometry's mystic trails.