因为π/4<α+β<π,所以sin(α+β)>0,
因为
-π/2<π/4-α<0,
cos(π/4-α)=3/5,
所以sin（π/4-α)= -4/5；
因为
3π/4<β+3π/4<π
sin(3π/4+β)=5/13
所以cos(3π/4+β)= -12/13
sin(3π/4+β-(π/4 -α))=sin(α+β+π/2)= - cos(α+β)=(5/13)*(3/5)-(-12/13)*(-4/5)=-33/65
sin(α+β)=√(1-(33/65)∧2)=(√3116)/65