We have measured the temperature dependence of the resistivity ρ of an epitaxial (YBa₂Cu₃O_7-δ)₂₄/(PrBa₂Cu₃O_7-δ)₂ multilayer nanometre film at several magnetic fields parallel to the c-axis and at a constant magnetic field H = 4 T. The measurements were taken for various angles α between the magnetic field and the surface of the film with H in the plane between the measuring current I and the c-axis, and for various angles θ between the magnetic field H and the surface of the film (ab-plane) with H ⊥ I. The resistive broadening depends mainly on the effective applied magnetic field H_e = H×(sin²θ + cos²θ/γ²)^1/2 with respect to the c-axis, and shows a three-dimensional anisotropic behaviour, where γ is the anisotropy parameter. The angular dependences of the peak temperature T_p and the activation energy U_e for angle θ and α>5° are in agreement with the effective mass model, namely T_p(0)-T_p(H,θ) ∝(sin²θ + cos²θ/γ²)^1/2n and U_e∝H_e^-m with γ = 10, n = 1.31 and m = 0.87. The dissipative resistivity below T_p for various magnetic fields can be scaled onto a single curve by thermally activated flux motion. When the applied field tilts the CuO₂ plane, the angular dependences of T_p and U_e reveal a lock-in transition, showing that the flux lines were trapped in the non-superconducting PrBCO layers.