Compute the (square)distances between the points, if they are equal, then you have

an equilateral triangle.

first two:

D^2=(4-1)^2+(5-7)^2+(2-3)^2=9+4+1=14

first and third:

D^2=(4-2)^2+(5-4)^2+(2-5)^2=4+1+9=14

second and third:

D^2=(1-2)^2+(7-4)^2+(3-5)^2=1+9+4=14

QED

RonL