Spin-averaged asymmetries in the azimuthal distributions of positive and negative hadrons produced in deep inelastic scattering were measured using the CERN SPS longitudinally polarised muon beam at 160 GeV/c and a (LiD)-Li-6 target. The amplitudes of the three azimuthal modulations cos phi(h), cos 2 phi(h) and sin phi(h) were obtained binning the data separately in each of the relevant kinematic variables x, z or p(T)(h), and binning in a three-dimensional grid of these three variables. The amplitudes of the cos phi(h) and cos 2 phi(h) modulations show strong kinematic dependencies both for positive and negative hadrons.