$If\tan 5\theta =\cot 2\theta$then the principal value of $\theta$ =

$$\begin{gathered} \tan 5\theta =\cot 2\theta =\tan (\frac{\pi }{2}-2\theta ) \\ \Rightarrow 5\theta =n\pi +\frac{\pi }{2}-2\theta \Rightarrow 7\theta =n\pi +\frac{\pi }{2} \end{gathered}$$

$\Rightarrow \theta =\frac{n\pi }{7}+\frac{\pi }{14},$ where  $n\in Z,$ but $n\ne 3,10,17,\dots .$
Where tan 5θ is not defined