ISL 2022 G1

Let $A B C D E$ be a convex pentagon such that $B C=D E$. Assume there is a point $T$ inside $A B C D E$ with $T B=T D, T C=T E$ and $\angle T B A=\angle A E T$. Let lines $C D$ and $C T$ intersect line $A B$ at points $P$ and $Q$, respectively, and let lines $C D$ and $D T$ intersect line $A E$ at points $R$ and $S$, respectively. Assume that points $P, B, A, Q$ and $R, E, A, S$ respectively, are collinear and occur on their lines in this order. Prove that the points $P, S, Q, R$ are concyclic. (Slovakia)