Hanoi Open Mathematics Competition 2013 Senior Question 7

Let \(ABC\) be equilateral, and let \(M\) lie inside it with \(MA^2=MB^2+MC^2\). Draw equilateral \(ACD\), where \(D\ne B\). Let \(N\) lie inside \(ACD\) so that \(AMN\) is equilateral. Determine \(\angle BMC\).