Hanoi Open Mathematics Competition 2008 Senior Question 9

Consider a triangle \(ABC\). For every \(M\in BC\), define \(N\in CA\), \(P\in AB\) such that \(APMN\) is a parallelogram. Let \(O=BN\cap CP\). Find \(M\in BC\) such that \(\angle PMO=\angle OMN\).