Let \(ABCDE\) be a convex pentagon such that \(BC=DE\). Assume that there is a point \(T\) inside \(ABCDE\) with \(TB=TD,TC=TE\) and \(\angle ABT = \angle TEA\). Let line \(AB\) intersect lines \(CD\) and \(CT\) at points \(P\) and \(Q\), respectively. Assume that the points \(P,B,A,Q\) occur on their line in that order. Let line \(AE\) intersect \(CD\) and \(DT\) at points \(R\) and \(S\), respectively. Assume that the points \(R,E,A,S\) occur on their line in that order. Prove that the points \(P,S,Q,R\) lie on a circle.