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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.

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