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cos(x)+sin(y)=-(sqrt(1/3)); sin(x)*sin(y)=1/(sqrt(3)); cos(y)=-1/(sqrt(3))

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The solution

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                      1  
cos(x) + sin(y) = - -----
                      ___
                    \/ 3 
$$\sin{\left(y \right)} + \cos{\left(x \right)} = - \frac{1}{\sqrt{3}}$$
                  1  
sin(x)*sin(y) = -----
                  ___
                \/ 3 
$$\sin{\left(x \right)} \sin{\left(y \right)} = \frac{1}{\sqrt{3}}$$
          -1  
cos(y) = -----
           ___
         \/ 3 
$$\cos{\left(y \right)} = - \frac{1}{\sqrt{3}}$$
cos(y) = -1/sqrt(3)