kill(all)$

van=facebook.com/LearningCalculus$

A(x,y):=matrix([sin(x),sin(y)],[cos(x),cos(y)]);

X:matrix([1],[1])$

B:matrix([sqrt(2)/2],[sqrt(6)/2])$

F(x,y):=A(x,y).X - B;

abs(F(x,y)[1])+abs(F(x,y)[2]);

G(x,y):=abs(sin(y)+sin(x)-1/sqrt(2))+abs(cos(y)+cos(x)-sqrt(6)/2);

a:24;

for i: 1 thru a step 2 do
    for j: 2 thru a step 2 do
        for k: 1 thru a step 2 do
            for l: 2 thru a step 2 do
                if abs((float(G((i/j)*%pi,(k/l)*%pi)))) < 0.000001 then
                    print("Answer: ", "a: ", i/j*%pi, "b: ", k/l*%pi,
                          "Answer: ", sin(i/j*%pi+k/l*%pi),
                          " Error: ", float((G((i/j)*%pi,(k/l)*%pi))));