We study the manipulation of the photoelectron spin-polarization in Bi$_2$Se$_3$ by spin- and angle-resolved photoemission spectroscopy. General rules are established that enable controlling the spin-polarization of photoemitted electrons via light polarization, sample orientation, and photon energy. We demonstrate the $pm$100% reversal of a single component of the measured spin-polarization vector upon the rotation of light polarization, as well as a full three-dimensional manipulation by varying experimental configuration and photon energy. While a material-specific density-functional theory analysis is needed for the quantitative description, a minimal two-atomic-layer model qualitatively accounts for the spin response based on the interplay of optical selection rules, photoelectron interference, and topological surface-state complex structure. It follows that photoelectron spin-polarization control is generically achievable in systems with a layer-dependent, entangled spin-orbital texture.
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