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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