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$$\lt br/\gt \tan^{-1}x+\tan^{-1}y\lt br/>=\begin{cases}\lt br/\gt \tan^{-1}\!\Bigl(\frac{x+y}{1-xy}\Bigr), & xy\lt 1,\\
-\frac{\pi}{2}, & xy=1,\;x+y\lt 0.\lt br/\gt \end{cases}\lt br/\gt $$
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$$\lt br/\gt \tan^{-1}x+\tan^{-1}y\lt br/>=\begin{cases}\lt br/\gt \tan^{-1}\!\Bigl(\frac{x+y}{1-xy}\Bigr), & xy\lt 1,\\
-\frac{\pi}{2}, & xy=1,\;x+y\lt 0.\lt br/\gt \end{cases}\lt br/\gt $$
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