Because ABCD is a diamond.

So angle B= angle D=60 degrees. Angle A= angle BCD

Triangle BCM is equal to triangle DCN.

Angle A+ angle BCD=360 degrees-angle B- angle d.

2 angle A = 2° angle BCD=240 degrees.

Angle A= angle BCD= 120 degrees.

MC=NC

CMN angle = CNM angle, MCN angle =60 degrees.

So the triangle CMN is an equilateral triangle.