If set $A=\left\{x: \tan x=\sec x, x\in \left[\mathrm{0,4}\pi \right]\right\}$ and set $B=\left\{x: {\sin }^{2}x=1, x\in \left[\mathrm{0,4}\pi \right]\right\}$, then

For $A, \frac{\sin x}{\cos x}=\frac{1}{\cos x}\Rightarrow \sin x=1$
$\therefore x=\frac{\pi }{2}, \frac{5\pi }{2}$
but at $x=\frac{\pi }{2}, \frac{5\pi }{2}$

$\tan x, \sec \theta$ is not defined
$\therefore A=\varphi$
for $B, \sin x=1, \sin x=-1$
$x=\frac{\pi }{2},\frac{5\pi }{2} \mathrm{or} x=\frac{3\pi }{2},\frac{7\pi }{2}$
$\therefore B=\left\{\frac{\pi }{2},\frac{3\pi }{2},\frac{5\pi }{2},\frac{7\pi }{2}\right\}$
$\therefore n\mathrm{}\left(A\times B\right)=0$