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# We have, $2{\tan ^{ – 1}}(\cos \theta ) = {\tan ^{ – 1}}(2{\mathop{\rm cosec}\nolimits} \theta )$$\Rightarrow$${\tan ^{ – 1}}\left( {\frac{{2\cos \theta }}{{1 – {{\cos }^2}\theta }}} \right) = {\tan ^{ – 1}}(2{\mathop{\rm cosec}\nolimits} \theta )$$\Rightarrow \left( {\frac{{2\cos \theta }}{{{{\sin }^2}\theta }}} \right) = (2{\mathop{\rm cosec}\nolimits} \theta )$$ \Rightarrow (\cot \theta \cdot 2{\mathop{\rm cosec}\nolimits} \theta ) = (2{\mathop{\rm cosec}\nolimits} \theta ) \Rightarrow \cot \theta = 1$$\Rightarrow$$\cot \theta = \cot \frac{\pi }{4} \Rightarrow \theta = \frac{\pi }{4}$

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