Angles of visible moiré patterns are observed experimentally. Experiments were made across the angular range 0 - 90° in a wide range of parameters. Two kinds of clusterization were observed, ray and discrete. In rational cells (LCD pixels), the moiré patterns appear at a few fixed discrete angles. The list of preferable moiré-less angles is presented basing on the experimental data; preferable areas in the parameter space are found. The problem of minimization of the moiré effect is formulated as the Diophantine inequality with complex coefficients. The classification of moiré angles basing on the probability of the moiré effect can be practically useful.