6. Let $q$ be a 7th root of 1, then $\frac{q}{1+q^{2}}+\frac{q^{2}}{1+q^{4}}+\frac{q^{3}}{1+q^{6}}=$
6. When $q=1$, the original expression $=\frac{3}{2}$  
When $q \neq 1$, the original expression $=\frac{q}{1+q^{2}}+\left(\frac{q^{2}}{1+q^{4}}+\frac{1}{q^{3}+q^{4}}\right)=\frac{q}{1+q^{2}}+\frac{q^{4}+q^{6}}{q^{3}+1}=-2$