Three, Find the solutions to the following equation (20 points)
$$
x^{5}-5 x^{4}-10 x^{3}+10 x^{2}+5 x-1=0
$$
Let $\tan \theta=t$,
then $\tan 2 \theta=\frac{2 t}{1-t^{2}}$,
$$
\tan 3 \theta=\frac{3 t-t^{3}}{1-3 t^{2}} \Rightarrow \tan 5 \theta=\frac{5 t-10 t^{3}+t^{5}}{1-10 t^{2}+5 t^{4}}
$$

So $\tan 5 \theta=1 \Leftrightarrow$ the original equation.
Let $\tan 5 \theta=1$
$$
\Rightarrow 5 \theta=\frac{\pi}{4} + k \pi, k=0,1,2,3,4,
$$

So $\theta=\frac{\pi}{20}+\frac{k}{5} \pi$,
So $t=\tan \left(\frac{\pi}{20}+\frac{k}{5} \pi\right)$.
So $x_{k}=\tan \left(\frac{\pi}{20}+\frac{k}{5} \pi\right), k=0,1,2,3,4$.