whats The value of cot^-1 (tan pi/7)?

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Please find below the solution to the asked query:

$$\begin{gathered} {\cot }^{-1}\mathrm{x}+{\tan }^{-1}\mathrm{x}=\frac{\mathrm{\pi }}{2} \\ \Rightarrow {\cot }^{-1}\left(\tan \left(\frac{\mathrm{\pi }}{7}\right)\right)=\frac{\mathrm{\pi }}{2}-{\tan }^{-1}\left(\tan \left(\frac{\mathrm{\pi }}{7}\right)\right) \\ \mathrm{since}, {\tan }^{-1}\left(\mathrm{tanx}\right)=\mathrm{x} \\ \mathbf{\Rightarrow }\frac{\mathbf{\pi }}{\mathbf{2}}\mathbf{-}\frac{\mathbf{\pi }}{\mathbf{7}}\mathbf{=}\frac{\mathbf{7}\mathbf{\pi }\mathbf{-}\mathbf{2}\mathbf{\pi }}{\mathbf{14}}\mathbf{=}\frac{\mathbf{5}\mathbf{\pi }}{\mathbf{14}} \end{gathered}$$

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