Duarti wrote: Solve the system of equations $x+y+z=\pi$ $\tan x\tan z=2$ $\tan y\tan z=18$ Let $u=\tan x$, $v=\tan y$ and $w=\tan z$ so that system is : $w=\frac{u+v}{uv-1}$ and $uw=2$ and $vw=18$ With easy solutions $\left(\frac 12,\frac 92,4\right)$ and $\left(-\frac 12,-\frac 92,-4\right)$ And so : $\boxed{\text{S1 : }(x,y,z)=(\arctan \frac 12+m\pi,\arctan \frac 92+n\pi,\arctan 4-(m+n)\pi)}$, whatever are $m,n\in\mathbb Z$ $\boxed{\text{S2 : }(x,y,z)=(-\arctan \frac 12+m\pi,-\arctan \frac 92+n\pi,-\arctan 4-(m+n-2)\pi)}$, whatever are $m,n\in\mathbb Z$