sin(α+β)=-3/5,sin(β-π/4)=12/13
∵α+β∈(3π/2,2π),β-π/4∈(π/2,3π/4)
∴cos(α+β)=√[1-sin^2(α+β)]=4/5
cos(β-π/4)=-√[1-sin^2(β-π/4)]=-5/13
sin(α+π/4)=sin[(α+β)-(β-π/4)]
=sin(α+β)cos(β-π/4)-cos(α+β)sin(β-π/4)
=-33/65
∵α+π/4∈(π,5π/4)
cos(α+π/4)=-√[1-sin^2(α+π/4)]=-56/65
∴tan(α+π/4)=sin(α+π/4)/cos(α+π/4)=33/56