MathNet 1986 — Part 01 Question 23

$A$ and $B$ are fixed points outside a sphere $S$. $X$ and $Y$ are chosen so that $S$ is inscribed in the tetrahedron $ABXY$. Show that the sum of the angles $AXB$, $XBY$, $BYA$ and $YAX$ is independent of $X$ and $Y$.