Consider:
syms a b D S L X Y Z
e1 = D == -(X*cos(a)+Z*sin(a))*cos(b) - Y*sin(b);
e2 = S == (X*cos(a)+Z*sin(a))*sin(b) - Y*cos(b);
e3 = L == X*sin(a) - Z*cos(a);
S = solve([e1 e2 e3],[X Y Z]);
% observe results
S.X
S.Y
S.Z
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