28. Solve the system of equations: $\left\{\begin{array}{l}\operatorname{tg} x \operatorname{tg} y=\frac{1}{6} \\ \sin x \sin y=\frac{1}{5 \sqrt{2}}\end{array}\right.$
28. Dividing the second equation by the first, we get $\cos x \cos y=\frac{6}{5 \sqrt{\overline{2}}}$.

Subtracting the second equation from the result, we get

$$
\cos (x+y)=\frac{1}{\sqrt{2}}, \text { from which } x+y= \pm \frac{\pi}{4}+2 \pi k
$$

Similarly, $\cos (x-y)=\frac{7}{5 \sqrt{2}}$. From which $x-y= \pm \arccos \frac{7}{5 \sqrt{2}}+2 \pi k$.