7.3. In triangle $A B C$, the median $A M$ 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 $A M$ and $O Q$ intersect at point $R$, and $\frac{O R}{M R}=\sqrt{7} \frac{Q R}{A R}$. Find the cosine of the difference in the measures of angles $A B C$ and $A C B$, given that $\angle B A C=\frac{\pi}{3}$. Round your answer to the nearest hundredth if necessary.
Answer: $-0.13$ (exact value: $-1 / 8$ ).