If \( a \) is real constant and \( A, B, C \) are variable angles and \( \sqrt{a^{2}-4} \tan A...

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If \( a \) is real constant and \( A, B, C \) are variable angles and \( \sqrt{a^{2}-4} \tan A+a \tan B+\sqrt{a^{2}+4} \tan C=6 a \) then find the least value of \( \tan ^{2} A+\tan ^{2} B+\tan ^{2} C \).
(a) 15
(b) 12
(c) 18
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