4 $[\quad$ Equifacetal Tetrahedron $\quad]$

In the triangular pyramid $A B C D$, the sums of the three dihedral angles at each of the vertices $B$ and $C$ are $180^{\circ}$ and $A D=B C$. Find the volume of the pyramid if the area of the face $B C D$ is 100, and the distance from the center of the circumscribed sphere to the plane of the base $A B C$ is 3.