Recursive Triangles

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A sequence of triangles \(\{\triangle A_iB_iC_i \}_{i=1}^{\infty } \) is defined recursively as follows:

  • The internal bisector of \(\angle C_iA_iB_i\) intersects the circumcircle of \(\triangle A_iB_iC_i\) at \(A_{i+1} \).

  • The internal bisector of \(\angle A_iB_iC_i\) intersects the circumcircle of \(\triangle A_iB_iC_i\) at \(B_{i+1}\).

  • The internal bisector of \(\angle B_iC_iA_i\) intersects the circumcircle of \(\triangle A_iB_iC_i\) at \(C_{i+1} \).

Given that \(\angle B_1A_1C_1= 60°\), find the value of \(\angle C_{2013} A_{2014} B_{2013} \) in degrees.

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