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solve:

cos^-1([x²-1]/[x²+1]) + tan^-1[(2x)/(x²-1)]=2pi/3

$\cos^{- 1} (\frac{x^{2} - 1}{x^{2} + 1}) + \tan^{- 1} (\frac{2 x}{x^{2} - 1}) = \frac{2 π}{3} π - \cos^{- 1} (\frac{1 - x^{2}}{1 + x^{2}}) - \tan^{- 1} (\frac{2 x}{1 - x^{2}}) = \frac{2 π}{3} - 2 \tan^{- 1} x - 2 \tan^{- 1} x = \frac{- π}{3} \tan^{- 1} x = \frac{π}{12} \Rightarrow x = \tan \frac{π}{12}$

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