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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