So sinx+cosx=siny+cosy,

Square both sides to get1+2sinxcosx =1+2sinycosy,

So 2sinxcosx=2sinycosy, that is, sin2x=sin2y,

So 2x=2y or 2x+2y=π,

2x+2y=π from sinx-siny=-2/3，

So x+y=π/2,

sin(x+y)=sin(π/2)= 1