75. At the base of the triangular pyramid $A B C D$ lies an equilateral triangle $A B C$. The face $B C D$ forms an angle of $60^{\circ}$ with the base plane. On the line passing through point $D$ perpendicular to the base, lies the center of a sphere with a unit radius, which touches the edges $A B$, $A C$, and the face $B C D$. The height of the pyramid $D H$ is half the length of the base side. Find the volume of the pyramid.
75. $\frac{9 \sqrt{3}}{8}$.