Answer
$x = \frac{\pi}{4} + k\pi $, where $k$ is an integer.
Work Step by Step
The line $y-x=2$ or $y=x+2$ has slope $1$.
Furthermore, $y' = 3-sec^2(x)$
We then solve for all values of $x$ for which $y' = 1$:
$ 3-sec^2(x)=1$
$sec^2(x) = 2$
$sec(x) = \pm \sqrt{2}$
$x = \frac{\pi}{4} + k\pi$, where $k$ is an integer.
