Expression for sin(1 degree)?

I have heard that it is possible to derive an expression for $\displaystyle sin(1^\circ)$. I have tried myself, but I have only gotten to the part where I shall derive an expression for $\displaystyle sin(10^\circ)$ from the expression of $\displaystyle sin(30^\circ)$. To get $\displaystyle sin(30^\circ)$ I had to use complex numbers to first get an expression for $\displaystyle tan(30^\circ)$, but when I try to do the same thing again I get the equation $\displaystyle x^3-\sqrt{3}x^2-3x = -\sqrt{\frac{1}{3}}$ (where $\displaystyle x = tan(10^\circ)$), but I don't know how to solve that. How do I continue?