Number of values of $x\in \left[0,4\pi \right]$ and satisfying $\sqrt{2}\sec x+\tan x=1$ is

We can write the given equation as  $\sqrt{2}=\cos x-\sin x$

$\Rightarrow \frac{1}{\sqrt{2}}\cos x-\frac{1}{\sqrt{2}}\sin x=1$

$\Rightarrow \cos \left(x+\frac{\pi }{4}\right)=1$

$\Rightarrow x+\frac{\pi }{4}=2n\pi ,n\in I$

$\Rightarrow x=\frac{7\pi }{4},\frac{15\pi }{4}$