7.4. In triangle $K L M$, the median $K P$ is drawn, point $O$ is the center of the circumscribed circle around it, and point $Q$ is the center of the inscribed circle in it. Segments $K P$ and $O Q$ intersect at point $R$, and $\frac{O R}{P R}=\sqrt{14} \frac{Q R}{K R}$. Find the product of the sines of the angles $K L M$ and $K M L$, given that $\angle L K M=\frac{\pi}{3}$. Round the answer to the nearest hundredth if necessary.
Answer: 0.63 (exact value: $5 / 8$).

Note. The exact values $0.125, -0.375, -0.125$ and 0.625 are also accepted as correct.