Solve w=operatorname{arctg}(3u^2-6v)

$$w = \operatorname { arctg } ( 3 u ^ { 2 } - 6 v )$$

Solve for u

$$u=\frac{\sqrt{3\left(\tan(w)+6v\right)}}{3}$$

$$u=-\frac{\sqrt{3\left(\tan(w)+6v\right)}}{3}\text{, }\exists n_{2}\in \mathrm{Z}\text{ : }\left(w\geq -\arctan(6v)+\pi n_{2}\text{ and }w\leq \frac{\pi \left(2n_{2}+1\right)}{2}\right)\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }w=\frac{\pi \left(2n_{1}+1\right)}{2}\text{ and }|w|\leq \frac{\pi }{2}$$

Solve for v

$$v=\frac{-\tan(w)+3u^{2}}{6}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }w=\pi n_{1}+\frac{\pi }{2}\text{ and }|w|\leq \frac{\pi }{2}$$