They're to do with symmetry of sine.
If you think about your problem, you essentially have a horizontal line intersecting some curve of sine. If you imagine you have
21=sin(x) then if you were to sketch the line and the curve between 0 and 2pi then you would see that the line intersects the sine curve at
x=arcsin(1/2) as well as some point later on. Due to symmetry of sine around
x=2π, you get that other point of intersection by going
π radians along the x-axis from 0, then turning around and going
−arcsin(1/2) radians. So your two solutions here would be
x=arcsin(1/2) and
x=π−arcsin(1/2).
Since sine repeats the same pattern every
2π, we can generalise by saying intersections happen every
2π which turns our equations into
x=2πn+arcsin(1/2) and
x=2πn+π−arcsin(1/2) where of course n can be any integer as it determines which period of sine you are referring to. You should choose it accordingly to your range.
Anyway, that's just a stupid long explanation for something very simple, and avoids the nonsense of CAST. Applies in the same way for degrees using conversion.