# Calculus is not needed II

Geometry Level 4

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

If $$\alpha$$ is real constant and $$A, B$$ and $$C$$ are variable angles satisfying the condition above, then find the least value of $$\tan ^{ 2 }{ A } +\tan ^{ 2 }{ B } +\tan ^{ 2 }{ C }$$

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