I have tired using an expression for $\displaystyle \tan 4 \theta $ and got nowhereProve that $\displaystyle \tan \frac{\pi}{15}$ is a root of the equation.

$\displaystyle t^4 -6 \sqrt{3}t^3 +8t^2 + 2 \sqrt{3} t -1 =0$

Give the other roots in the form $\displaystyle \tan \frac{r \pi}{15}$

Thanks in Advance

Bobak