  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.
