# How do I get the solutions of a cubic equation in trigonometric form?

I know $x^3-3 x+1=0$ has three roots that can be expressed in trigonometric form: $\{2\sin(10^\circ),\,-2\cos(20^\circ),\,2\cos(40^\circ)\}$.

How can I get this result with Mathematica?

ComplexExpand@

(ComplexExpand@Solve[x^3 - 3 x + 1 == 0, x] /. Pi/9 -> t // TrigFactor) /. t -> Pi/9