已知 sin(α−β)=13,tanα=3tanβ\sin \left( {\alpha - \beta }\right) = \frac{1}{3},\tan \alpha = 3\tan \betasin(α−β)=31,tanα=3tanβ ,则 sin(α+β)=\sin \left( {\alpha + \beta }\right) =sin(α+β)= （ ）A. 16\frac{1}{6}61B. 13\frac{1}{3}31C. 12\frac{1}{2}21D. 23\frac{2}{3}32