We can express values for (e.g. 22,5° or 45° or 54°,90°....) with a combination of square roots and basic calculating operations, however are they all expressible in such a way (=> are all algebraic?) Or are non-obvious trigonometric values (e.g. cos(3°)) transcendental numbers?
With very poor math skills, these are my thoughs on values that are not multiples of 5 or are already known for being algebraic.
All help is appreciated.