# Trigonometric warping

Geometry Level 4

This question is flagged because I believe that $$\alpha, \beta, \gamma$$ should be angles in a triangle.

If $$|\cos{\alpha}\cos{\beta}\cos{\gamma}|=\frac{2}{3}$$. Then the maximum value of $$\tan{\alpha}\tan{\beta}+\tan{\beta}\tan{\gamma}+\tan{\gamma}\tan{\alpha}$$ is $$X$$.

Find $$24X$$.

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