In color reproduction, the most troublesome moire pattern is the second-order moire, or the three-color moire, usually produced by mixing of cyan, magenta and black halftone outputs. A classical 3-color zero-moire solution is using three identical cluster halftone screens with different rotations: 15, 45 and 75°, respectively. However, for most digital printing devices, the size and shape of halftone screens are constrained by the "digital grid", which defines the locations of printed dots; and therefore, an exact 15 or 75° rotation of a cluster screen is impossible. Although there are many alternative approaches for moire-free color halftoning, most of them only provide approximate solutions and/or have a tendency to generate additional artifacts associated with halftone outputs. The difficulty to achieve moire-free color halftoning is greatly relieved by using non-orthogonal halftone screens, i.e., screens in general parallelogram shapes. In this paper, a general condition for 3-color zero-moire solutions is derived. A procedure using integer equations to search moire-free solutions for different applications is also described.