The solution set of the equation $\tan (\pi \tan x)=\cot (\pi \cot x)$ is

$\tan (\pi \tan x)=\tan (\pi /2-\pi \cot x)$

$\begin{array}{l}\Rightarrow \pi \tan x=\pi /2-\pi \cot x\Rightarrow \tan x+\cot x=1/2\\ \Rightarrow 2{\tan }^{2}x-\tan x+2=0\\ \Rightarrow \tan x=\frac{1+\sqrt{1-16}}{4}\end{array}$

which does not give real values of tan x.