Školjka

%V0 Let $M$ and $N$ be two points inside triangle $ABC$ such that $$\angle MAB = \angle NAC\quad \mbox{and}\quad \angle MBA = \angle NBC.$$ Prove that $$\frac {AM \cdot AN}{AB \cdot AC} + \frac {BM \cdot BN}{BA \cdot BC} + \frac {CM \cdot CN}{CA \cdot CB} = 1.$$