3. Let $\varepsilon$ be a 7th root of 1, compute: $\frac{\varepsilon}{1+\varepsilon^{2}}+\frac{\varepsilon^{2}}{1+\varepsilon^{4}}+\frac{\varepsilon^{3}}{1+\varepsilon^{6}}$.
3. From the complex square root formula, we know that $\varepsilon^{7}=1, \varepsilon=1$ or imaginary roots. When $\varepsilon=1$, the original expression $=\frac{3}{2}$; when $\varepsilon$ is an imaginary root, the original expression $=-2$. Therefore, the required values are $\frac{3}{2}$ or -2.