G3.3 Given that $\tan x+\tan y+1=\cot x+\cot y=6$. If $z=\tan (x+y)$, find the value of $z$.
$\begin{array}{l}\tan x+\tan y+1=\frac{\tan y+\tan x}{\tan x \tan y}=6 \\ \tan x+\tan y=5 ; \tan x \tan y=\frac{5}{6} \\ \tan (x+y)=\frac{\tan x+\tan y}{1-\tan x \tan y}=\frac{5}{1-\frac{5}{6}}=30\end{array}$