tanα=1
α=kπ+π/4
3sinβ=sin(2α+β)=sin(π/2+β)=cosβ
tanβ=1/3
tan(α+β)=(tanα+tanβ)/(1-tanαtanβ)=(1+1/3)/(1-1*1/3)=2
所以：
tan(α+2β)=(tan(α+β)+tanβ)/(1-tan(α+β)tanβ)=(1/3+2)/(1-2*1/3)=7