( a + b + c) (a + b - c) = 3ab
[ (a + b) + c ] [(a + b) - c ] = 3ab
(a + b)^2 - c^2 = 3ab
a^2 + 2ab + b^2 - c^2 = 3ab
a^2 + b^2 = ab + c^2 (1)
Using the Law of Cosines
c^2 = [a^2 + b^2] - 2(a)(b) cos C (2)
Sub (1) into (2) and we have that
c^2 = [ ab + c^2] - (2ab) cos C
c^2 = ab + c^2 - (2ab) cos C subtract c^2 from both sides
0 = ab - 2ab cos C subtract ab from both sides
-ab = - 2ab cos C divide both sides by -2ab
1/2 = cos C
arccos (1/2) = C = 60°
Thanks to asinus for the hint of applying the Law of Cosines !!!