6.57. The vertex $S$ of the triangular pyramid $S A B C$ coincides with the vertex of a cone, and the points $A, B$ and $C$ lie on the circumference of its base. The dihedral angles at the edges $S A, S B$ and $S C$ are $\alpha, \beta$ and $\gamma$. Find the angle between the plane $S B C$ and the plane tangent to the surface of the cone along the generatrix $S C$.
6.57. Let $O$ be the center of the base of the cone. In the trihedral angles $S B O C, S C O A$, and $S A O B$, the dihedral angles at the edges $S B$ and $S C, S C$ and $S A, S A$ and $S B$ are equal. Denote these angles by $x, y$, and $z$. Then $\alpha=y+z, \beta=z+x$ and $\gamma=x+y$. Since the plane $SCO$ is perpendicular to the plane tangent to the surface of the cone along the generatrix $S C$, the desired angle is

$$
\frac{\pi}{2}-x=\frac{\pi+\alpha-\beta-\gamma}{2}
$$