If is real constant and and are variable angles and

MATHEMATICS · Subjective · AoPS · Mathematics · More Inequalities · More Inequalities

Problem

a

is real constant and

A, B

and

C

are variable angles and

\sqrt{a^2 - 4} \tan A + a \tan B + \sqrt{a^2 + 4} \tan C = 6a

, then find the least value of

\tan^2 A + \tan^2 B + \tan^2 C