VMO 1994 Problem 3

Define the sequence $x_0$, $x_1$, $x_2$, ... by $x_0$ = a, where 0 < a < 1, $x_{n+1}$ = 4/π$^2$ ($cos^{-1}x_n$ + π/2) $sin^{-1}x_n$. Show that the sequence converges and find its limit.