6. Let the circumradius of $\triangle A B C$ be $R, \frac{a \cos A+b \cos B+c \cos C}{a \sin B+b \sin C+c \sin A}=\frac{a+b+c}{9 R}$. Here $a, b, c$ are the sides opposite to $\angle A, \angle B, \angle C$ respectively. Try to find the sizes of the three interior angles of $\triangle A B C$.