Suppose $3n$ is an angle between $0$ and $90$ degrees and that $n$ is an integer. By considering half squares and half equilateral triangles it's easy to obtain expressions for $\sin(3n)$ if $n=10$, $n=15$ and $n=20$. (By "expressions" I mean closed expressions involving addition, subtraction, multiplication, division and square roots.)
Using the addition/subtraction formulas for sine and cosine we can easily handle the cases $n=5$, and $n=25$ as well. I suppose that if I can find $\sin3$ then I can use these formulas to find $\sin(3n)$ for any $n$. Right? So my question is really this:
How do I find $\sin3$ (where the angle is measured in degrees)?