Just to clarify.
The question is reasonable: someone doesn't quite understand azimuths and RE theory.
The question was, why does the azimuth of sunrise always match the azimuth of sunset? (Actually, the negative of it, but never mind that.) It seems as though, if the Earth's axis is angled, the azimuths of these two events shouldn't be equal.
The reason why they're equal is simple: the Earth is a sphere, which is radially symmetrical. Therefore, sunrise and sunset azimuths will be symmetrical about the plane between the Earth and the Sun.
Here's a little experiment you can use to verify and illustrate this. Stand up straight and directly face a small light (or anything you can easily see in your peripheral vision) that's at roughly the height of your eyes. Turn your head left and right until it disappears from view*. You'll notice that (if you're reasonably symmetrical yourself, as most people are) that the light disappears at the same angle of head turn, left or right. Now bow forward a bit and repeat the experiment. You'll notice that the angle is less, but is still the same going right or left. The same is true of sunrise and sunset azimuths, and for the same reason: the Earth, like your head, is radially symmetrical.
This works for both sphere and cylinder since they're both radially symmetrical, so, by this little experiment, the Earth could be a cylinder and provide similar results. Of course, for a cylinder the azimuth table wouldn't vary by latitude.
* Ignoring blind spots -- if it disappears and then reappears as you turn further, that's a blind spot so ignore it. As usual, it's hard to ignore a blind spot unless you're aware of it.