Solve y=(1+cot^-13x)^3

$$y = ( 1 + \cot ^ { - 1 } 3 x ) ^ { 3 }$$

Solve for x

$$x=-\frac{\sin(1)\sin(\sqrt[3]{y})+\cos(1)\cos(\sqrt[3]{y})}{3\sin(-\sqrt[3]{y}+1)}$$

$$\nexists n_{2}\in \mathrm{Z}\text{ : }y=\frac{\left(2\pi n_{2}+\pi +2\right)^{3}}{8}\text{ and }\nexists n_{3}\in \mathrm{Z}\text{ : }y=\left(1-\pi n_{3}\right)^{3}\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }y=\frac{\left(-2\pi n_{1}+2-\pi \right)^{3}}{8}\text{ and }y\leq \left(\frac{\pi }{2}+1\right)^{3}\text{ and }y\geq \left(-\frac{\pi }{2}+1\right)^{3}$$

Solve for y

$$y=\left(\arctan(\frac{1}{3x})+1\right)^{3}$$

$$x\neq 0$$