Question 150
An acute isosceles triangle $ABC$ with $\angle B=\angle C=\alpha$ is the base of prism $ABCA_1B_1C_1$. Its lateral edge $AA_1$ is perpendicular to $AC$, and $\angle A_1AB=\beta\lt 90^\circ$. Given $AA_1=BC=a$, find the lateral surface area.