find all (x,y) such that

sin(x) + sin(y) = sin(x+y) and mod.(x) + mod.(y) = 1.

(0,1),(0,-1),(1,0),(-1,0) are the solutions of the equation.

becoz sin(x)+sin(y) = 2sin(x+y/2)cos(x-y/2)

and sin(x+y)= 2sin(x+y/2)cos(x+y/2)

putiing both of them equal 

we get cos(x-y/2) = cos(x+y/2)

then (x-y)/2= (x+y)/2 or (x-y)/2=-(x+y)/2 as cos(x)=cos(-x)

x=0 or y=0

Put these value in mod(x)+mod(y)=1 and get possible values of x and y.