∴∠CAE=∠CBD

That is ∠CAM=∠CBN.

∵AM=BN, BC=AC(△ABC is an equilateral triangle)

∴△ACM≌△BCN(SAS)

∴CM=CN

∠ACM=∠BCN

∠∠BCN+∠ACN =∠ACB = 60

Then ∠ ACM+∠ ACN = ∠ MCN = 60

∴△CMN is an equilateral triangle (an isosceles triangle has an angle of 60, so it is an equilateral triangle).