  In this paper, we discuss the commutativity of sums of two quasihomogeneous
Toeplitz operators on the Bergman space of the unit disc. Our main result goes
in the direction of the conjecture in "Bicommutants of Toeplitz operators" (by
I. Louhichi and N. V. Rao. Arch. Math. 91, 2008, 256-264)
