Quantum spin liquids are exotic states of matter that form when strongly frustrated magnetic interactions induce a highly entangled quantum paramagnet far below the energy scale of the magnetic interactions. Three-dimensional cases are especially challenging due to the significant reduction of the influence of quantum fluctuations. Here, we report the magnetic characterization of K2Ni2(SO4)(3) forming a three-dimensional network of Ni2+ spins. Using density functional theory calculations, we show that this network consists of two interconnected spin-1 trillium lattices. In the absence of a magnetic field, magnetization, specific heat, neutron scattering, and muon spin relaxation experiments demonstrate a highly correlated and dynamic state, coexisting with a peculiar, very small static component exhibiting a strongly renonnalized moment. A magnetic field B greater than or similar to 4 T diminishes the ordered component and drives the system into a pure quantum spin liquid state. This shows that a system of interconnected S = 1 trillium lattices exhibits a significantly elevated level of geometrical frustration.