If sin(x1)+sin(x2)+sin(x3)=3 then the average value of the sines is 1. Therefore each sine=1 or the sine of one is less than 1 and the other two are greater than 2. But sine cannot exceed 1 so all three sines must be equal to 1 and each angle is 90° or sum odd multiple of 90°. The sum of the cosines of the same angles must therefore be zero, because cos(90°)=0 as are all the odd multiples of 90°. The answer is 0.