若 sin(α+β)=cos2αsin(α−β)\sin \left( {\alpha + \beta }\right) = \cos {2\alpha }\sin \left( {\alpha - \beta }\right)sin(α+β)=cos2αsin(α−β) ,则 tan(α+β)\tan \left( {\alpha + \beta }\right)tan(α+β) 的最大值为（ ）A. 62\frac{\sqrt{6}}{2}26B. 64\frac{\sqrt{6}}{4}46C. 22\frac{\sqrt{2}}{2}22D. 24\frac{\sqrt{2}}{4}42