The Cheese for Mytsyk

While preparing dinner for Mytsyk, the host cut the cheese into identical rectangular parallelepipeds with a square base of side $A$ and height $B$.

However, Mytsyk preferred to enjoy cheese in slightly smaller portions. For this, he would always stand the offered piece upright on the table with its square face down and cut it into two parts. The knife was always placed along a diagonal of the square base, but he could not always split the piece exactly in half because the blade formed a dihedral angle of Z^\circ with the base.

Find the area $S$ of the section created by Mytsyk's cut.