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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!

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  • $\begingroup$ What are $A,B,C$, triangle angles? $\endgroup$ – Dr. Sonnhard Graubner Apr 21 '18 at 9:56
  • $\begingroup$ It isn't mentioned anywhere, I first of thought of that only seeing the general A, B, C angles, but it isn't mentioned. $\endgroup$ – Avinash Bhawnani Apr 21 '18 at 9:58
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Ahh, expansion of cos(a+b+c) will do it.

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