Spangles are "special" angles. They’re special because they show up a lot. Their values are given in this table 44 4 There are numerous problems with the formatting of this table which I will one day get around to fixing..
Don’t memorise the table! All you need to remember is that
From there, you can work out the rest of the values for , as the number being rooted just goes up by one (from to to ). The values of do the same thing, but the other way round. For , as
the values of can be computed from the values of .