IMO 1986 Problem 2

Given a point $P_0$ in the plane of the triangle $A_1A_2A_3$ . Define $A_s=A_{s-3}$ for all $s\ge4$ . Construct a set of points $P_1,P_2,P_3,\ldots$ such that $P_{k+1}$ is the image of $P_k$ under a rotation center $A_{k+1}$ through an angle $120^o$ clockwise for $k=0,1,2,\ldots$ . Prove that if $P_{1986}=P_0$ , then the triangle $A_1A_2A_3$ is equilateral.