Solve tan(θ)=3x^2-6x

$$\tan ( \theta ) =3 { x }^{ 2 } -6x$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{3\left(\left(3-i\right)e^{2i\theta }+\left(3+i\right)e^{-2i\theta }+6\right)}-6\cos(\theta )}{6\cos(\theta )}$$

$$x=\frac{\sqrt{3}\left(\sqrt{\left(3-i\right)e^{2i\theta }+\left(3+i\right)e^{-2i\theta }+6}+2\sqrt{3}\cos(\theta )\right)}{6\cos(\theta )}\text{, }\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}+\frac{\pi }{2}$$

Solve for x

$$x=\frac{\sqrt{3}\left(-\frac{\sqrt{\cos(\theta )\left(\sin(\theta )+3\cos(\theta )\right)}}{\cos(\theta )}+\sqrt{3}\right)}{3}$$

$$x=\frac{\sqrt{3}\left(\frac{\sqrt{\cos(\theta )\left(\sin(\theta )+3\cos(\theta )\right)}}{\cos(\theta )}+\sqrt{3}\right)}{3}\text{, }\exists n_{1}\in \mathrm{Z}\text{ : }\left(\theta \geq \pi n_{1}-\arcsin(\frac{3\sqrt{10}}{10})+\pi \text{ and }\theta <\frac{\pi \left(2n_{1}+3\right)}{2}\right)$$

Solve for θ

$$\theta =\pi +2n_{9}\pi +\left(-1\right)arcSin(6\left(36x^{2}+\left(-36\right)x^{3}+9x^{4}+1\right)^{-\frac{1}{2}}x+\left(-3\right)\left(36x^{2}+\left(-36\right)x^{3}+9x^{4}+1\right)^{-\frac{1}{2}}x^{2})\text{, }n_{9}\in \mathrm{Z}\text{, }\exists n_{42}\in \mathrm{Z}\text{ : }\left(\left(n_{9}>\left(-\frac{1}{4}\right)\left(\pi +\left(-2\right)arcSin(3x\left(2+\left(-1\right)x\right)\left(36x^{2}+\left(-36\right)x^{3}+9x^{4}+1\right)^{-\frac{1}{2}})+\left(-2\right)\pi n_{42}\right)\pi ^{-1}\text{ and }36x^{2}+\left(-36\right)x^{3}+9x^{4}+1>0\text{ and }not(3|x||2+\left(-1\right)x|\left(36x^{2}+\left(-36\right)x^{3}+9x^{4}+1\right)^{-\frac{1}{2}}>1)\right)\text{ and }\pi +2n_{9}\pi +\left(-1\right)arcSin(6\left(36x^{2}+\left(-36\right)x^{3}+9x^{4}+1\right)^{-\frac{1}{2}}x+\left(-3\right)\left(36x^{2}+\left(-36\right)x^{3}+9x^{4}+1\right)^{-\frac{1}{2}}x^{2})<\pi \left(n_{42}+\frac{3}{2}\right)\right)\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\pi +2n_{9}\pi +\left(-1\right)arcSin(6\left(36x^{2}+\left(-36\right)x^{3}+9x^{4}+1\right)^{-\frac{1}{2}}x+\left(-3\right)\left(36x^{2}+\left(-36\right)x^{3}+9x^{4}+1\right)^{-\frac{1}{2}}x^{2})=\frac{1}{2}\pi +\pi n_{1}$$

$$\theta =\left(-1\right)\left(arcSin(3x\left(2+\left(-1\right)x\right)\left(36x^{2}+\left(-36\right)x^{3}+9x^{4}+1\right)^{-\frac{1}{2}})+\left(-2\right)\pi n_{22}\right)\text{, }n_{22}\in \mathrm{Z}\text{, }\nexists n_{1}\in \mathrm{Z}\text{ : }\left(-1\right)\left(arcSin(3x\left(2+\left(-1\right)x\right)\left(36x^{2}+\left(-36\right)x^{3}+9x^{4}+1\right)^{-\frac{1}{2}})+\left(-2\right)\pi n_{22}\right)=\frac{1}{2}\pi +\pi n_{1}\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\left(-1\right)\left(arcSin(3x\left(2+\left(-1\right)x\right)\left(36x^{2}+\left(-36\right)x^{3}+9x^{4}+1\right)^{-\frac{1}{2}})+\left(-2\right)\pi n_{22}\right)=\frac{1}{2}\pi +\pi n_{1}$$