Sorry for asking a trivial question.
If I have to proof a statement like this:
$tan A tan B + tan B tan C + tan C tan A = 9$, then prove that the triangle ABC is equilateral.
My proof: If the triangle is equilateral then each angle must be equal to $\frac{π}{3}$, As $tan(\frac{π}{3}) = √3$, So 3+3+3=9, hence proved.
Is it a valid method of proof. If not, please tell how to tackle these problems.