<Qua-2025-778>, hint

Let D' on line AD such that AD=DD' =a and let C' on BC such that BC=CC'=a

Since <BEF=<BEC=60=<MED, M,E, C' are collinear ., DD'C'C is a square

In triangle MC'D , <MC'D'=60, <C'MD'=30.  C'M=2C'D'=2a=C'B.

Since <BC'M=30, <C'BM=<C'MB=75.

Since <BNC=75=<BME, B,M,N,E are concyclic, <MNB=<MEB=60, <EBN=<EMN=15

Hence <BMN=75-15=60=<MNB,  triangle BMN is equilateral.