Rectangles \(BCC_1B_2, CAA_1C_2, ABB_1A_2\)are erected outside an acute triangle ABC. Suppose that \(\angle BC_1C + \angle CA_1A + \angle AB_1B = 180^\circ\). Prove that lines \(B_1C_2, C_1A_2, \) and \(A_1B_2\) are concurrent.
