BG-MO 1968 Problem 6

Find the kind of a triangle if $$\frac{a\cos\alpha+b\cos\beta+c\cos\gamma}{a\sin\alpha+b\sin\beta+c\sin\gamma}=\frac{2p}{9R}.$$ ( $\alpha,\beta,\gamma$ are the measures of the angles, $a,b,c$ are the respective lengths of the sides, $p$ the semiperimeter, $R$ is the circumradius)

K. Petrov