The equation can be rearranged as:
\left[2 \cos \left(\frac{x-y}{2} \right) - \sin \left(\frac{x+y}{2} \right)\right]^2+\cos^2 \left(\frac{x+y}{2} \right)=0
solve for least values x and y...
2(sin x + sin y) - 2 cos(x-y)=3.
The equation can be rearranged as:
\left[2 \cos \left(\frac{x-y}{2} \right) - \sin \left(\frac{x+y}{2} \right)\right]^2+\cos^2 \left(\frac{x+y}{2} \right)=0