If $\lvert \cos A \cos B \cos C\rvert =\frac{2}{3}$, then find the maximum value of $\tan A \tan B + \tan B\tan C + \tan C\tan A$
I have no idea how to approach this question. I tried converting all tans to sin and cos, but that didn't help in any way. Then I thought maybe complex numbers will be used, but I wasn't able to understand how!
Ahh, expansion of cos(a+b+c) will do it.