3. Use three regular polygon tiles with equal side lengths to pave the ground, their vertices fit together perfectly to completely cover the ground. Let the number of sides of the regular polygons be $x$, $y$, and $z$. Then the value of $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$ is $\qquad$ .
3. $\frac{1}{2}$.

According to the problem, we have
$$
\frac{x-2}{x} \times 180^{\circ}+\frac{y-2}{y} \times 180^{\circ}+\frac{z-2}{z} \times 180^{\circ}=360^{\circ} \text {. }
$$

Simplifying, we get $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{2}$.