We study the angular dependence of the oscillations in WTe2 and ZrTe5 and report the first observation of a spin zero effect in topological materials. Experimental determination of the non-trivial Berry phase of topological materials largely relies on a phase analysis of quantum oscillations. In Dirac material ZrTe5, we observe a striking spin zero effect in certain field directions, i.e., vanishing oscillations accompanied with a phase inversion. This indicates that the Berry phase in ZrTe5 remains non-trivial for arbitrary field direction, in contrast with previous reports. Moreover, it is suggested that the Dirac band in ZrTe5 is likely transformed into a line-node other than Weyl points for the field directions at which the spin zero occurs. The results underline a largely overlooked spin factor when determining the Berry phase from quantum oscillations. In WTe2, a spin zero effect is also identified, which provides transport evidence for the spin splitting nature of the bands. A large Lande g-factor is estimated by the field dependence of the splitting.