Maybe I've just stared at this statement too long and I've missed something obvious. Nevertheless, here's the problem: Landau-Lifshitz vol. 1§16, problem 1.
Consider (classical) collision of two particles in center of mass coordinates. Before the collision, the particles are just traveling towards each other and in CM coordinates then the direction of the velocities of two particles should be opposite to each other, i.e. $$ \theta_1 = \theta_2 + \pi , $$ where $\theta_i$ is the angle between the velocity of particle $i$ and the coordinate axis.
However, in the solution in Landau-Lifshitz, they state that "In the C system, the corresponding angles are related by $\theta_1 = \pi - \theta_2$."
Is there a mistake in L-L? If not, can you explain me the relation above?