# Minimizing Tangents!

Geometry Level 4

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

If $$a$$ is a real constant and $$A,B,C$$ are variable angles such that the equation above is fulfilled, find the least value of $$\tan^{2}A + \tan^{2}B +\tan^{2}C$$.

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