Croatian Mathematical Olympiad 2010 Problem M-3

Unutar trokuta $ABC$ dana je točka $P$ takva da je

$$\measuredangle ABP = \measuredangle PCA = \frac{1}{3} (\measuredangle ABC + \measuredangle BCA).$$

Dokaži da je $\frac{|AB|}{|AC| + |PB|} = \frac{|AC|}{|AB| + |PC|}$.