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Antimatter particles such as positrons and antiprotons abound in the cosmos. Much less common are light antinuclei, composed of antiprotons and antineutrons, which can be produced in our galaxy via high-energy cosmic-ray collisions with the interstellar medium or could also originate from the annihilation of the still undiscovered dark-matter particles. On Earth, the only way to produce and study antinuclei with high precision is to create them at high-energy particle accelerators like the Large Hadron Collider (LHC). Though the properties of elementary antiparticles have been studied in detail, knowledge of the interaction of light antinuclei with matter is rather limited. This work focuses on the determination of the disappearance probability of \ahe\ when it encounters matter particles and annihilates or disintegrates. The material of the ALICE detector at the LHC serves as a target to extract the inelastic cross section for \ahe\ in the momentum range of 1.17≤p<10 GeV/c. This inelastic cross section is measured for the first time and is used as an essential input to calculations of the transparency of our galaxy to the propagation of 3He¯¯¯¯¯¯ stemming from dark-matter decays and cosmic-ray interactions within the interstellar medium. A transparency of about 50% is estimated using the GALPROP program for a specific dark-matter profile and a standard set of propagation parameters. For cosmic-ray sources, the obtained transparency with the same propagation scheme varies with increasing 3He¯¯¯¯¯¯ momentum from 25% to 90%. The absolute uncertainties associated to the 3He¯¯¯¯¯¯ inelastic cross section measurements are of the order of 10%−15%. The reported results indicate that 3He¯¯¯¯¯¯ nuclei can travel long distances in the galaxy, and can be used to study cosmic-ray interactions and dark-matter decays.