# Minima - II

Geometry Level 4

If $$\omega, \omega_{1}, \omega_{2}$$ are real variables such that $$\tan\omega+2\tan\omega_{1}+5\tan\omega_{2}=60$$, then find the minimum value of $$\tan^{2}\omega+\tan^{2}\omega_{1}+\tan^{2}\omega_{2}$$.

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