PAMO 2007 Problem 2

Let $A$ , $B$ and $C$ be three fixed points, not on the same line. Consider all triangles $AB'C'$ where $B'$ moves on a given straight line (not containing $A$ ), and $C'$ is determined such that $\angle B'=\angle B$ and $\angle C'=\angle C$ . Find the locus of $C'$ .