Solve x^3-6x^2+9x-1=0

$${ x }^{ 3 } -6 { x }^{ 2 } +9x-1=0$$

Solve for x (complex solution)

$$x=\frac{\left(-1+\sqrt{3}i\right)^{-\frac{4}{3}}\left(\sqrt[3]{2}\left(\sqrt[3]{2}\left(-1+\sqrt{3}i\right)^{\frac{8}{3}}+8\right)+8\left(-1+\sqrt{3}i\right)^{\frac{4}{3}}\right)}{4}\approx 0.120614758-8.326672685 \cdot 10^{-17}i$$

$$x=\frac{2^{\frac{2}{3}}\left(-1+\sqrt{3}i\right)^{-\frac{1}{3}}\left(\sqrt[3]{-1+\sqrt{3}i}+\sqrt[3]{2}\right)^{2}}{2}\approx 3.532088886+2.220446049 \cdot 10^{-16}i$$

$$x=\frac{\sqrt[3]{2}\left(1+\sqrt{3}i\right)^{-\frac{2}{3}}\left(2\times \left(2\left(1+\sqrt{3}i\right)\right)^{\frac{2}{3}}+\left(1+\sqrt{3}i\right)^{\frac{4}{3}}+2\sqrt[3]{2}\right)}{2}\approx 3.532088886-2.220446049 \cdot 10^{-16}i$$

Solve for x

$$x=4\left(\sin(\frac{\pi }{18})\right)^{2}\approx 0.120614758$$

$$x=4\left(\cos(\frac{\pi }{9})\right)^{2}\approx 3.532088886$$

$$x=2\left(\sin(\frac{\pi }{18})+1\right)\approx 2.347296355$$