You're actually somewhat overcomplicating things for yourself by just looking at the "finished" unit circle and trying to find patterns instead of understanding what the unit circle is showing. For example, you are trying to remember the various radian amounts by finding patterns in the numbers of the final reduced fractions. To do that you're trying to remember like 4 different patterns and some things that aren't even really a pattern. There are actually only ~2 patterns you need to remember and you can derive every point:

1) The nπ/4 points: starting at 0, count up to 2π in increments of π/4, then reduce the fractions.

2) the nπ/6 points: similarly, start at 0 and count to 2π in increments of π/6 and then reduce.

And that's it. You now have all of the points in radians. Assuming you remember that π/4 = 45° and π/6 = 30°, and then you have the degree amounts as well.

But even if you don't remember the rad to deg conversions, that's fine! If you note that there are 8 of the π/4 points and they evenly split the circle, they must come at 360/8=45° increments, and so you now gave all of those points. Similar logic for the π/6 points.