Recursive Triangles

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.