A vortex structure is predicted for Josephson-coupled superconductors in strong magnetic fields oriented near ab plane. The c axis component of the field forms an almost triangular pancake lattice inside the layers with the pancakes arranged in a zigzag structure along the c axis. This zigzag structure results in a sharp increase of the c-axis critical current and plasma frequency when the magnetic field deviates from ab orientation. These predictions are confirmed experimentally.