# 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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