If a real constant and \( \mathrm{A}, \mathrm{B} \) and \( \mathrm{...

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If a real constant and \( \mathrm{A}, \mathrm{B} \) and \( \mathrm{C} \) are variable angles
\( \mathrm{P} \) and \( \sqrt{\mathrm{a}^{2}-4} \tan \mathrm{A}+\mathrm{a} \tan \mathrm{B}+\sqrt{\mathrm{a}^{2}+4} \tan \mathrm{C}=6 \mathrm{a} \),

W then find the least value of \( \tan ^{2} \mathrm{~A}+\tan ^{2} \mathrm{~B}+\tan ^{2} \mathrm{C} \).
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