The base of the pyramid is a triangle $ABC$, in which $\angle ACB= 30^o$, and the length of the median from the vertex $B$ is twice less than the side $AC$ and is equal to $\alpha$ . All side edges of the pyramid are inclined to the plane of the base at an angle $a$. Determine the cross-sectional area of the pyramid with a plane passing through the vertex $B$ parallel to the edge $AD$ and inclined to the plane of the base at an angle of $\beta$,