We consider the neutrino (and antineutrino) flavors arriving at Earth for neutrinos produced in the annihilation of weakly interacting massive particles (WIMPs) in the Suns core. Solar-matter effects on the flavor propagation of the resulting $agt$ GeV neutrinos are studied analytically within a density-matrix formalism. Matter effects, including mass-state level-crossings, influence the flavor fluxes considerably. The exposition herein is somewhat pedagogical, in that it starts with adiabatic evolution of single flavors from the Suns center, with $theta_{13}$ set to zero, and progresses to fully realistic processing of the flavor ratios expected in WIMP decay, from the Suns core to the Earth. In the fully realistic calculation, non-adiabatic level-crossing is included, as are possible nonzero values for $theta_{13}$ and the CP-violating phase $delta$. Due to resonance enhancement in matter, nonzero values of $theta_{13}$ even smaller than a degree can noticeably affect flavor propagation. Both normal and inverted neutrino-mass hierarchies are considered. Our main conclusion is that measuring flavor ratios (in addition to energy spectra) of $agt$ GeV solar neutrinos can provide discrinination between WIMP models. In particular, we demonstrate the flavor differences at Earth for neutrinos from the two main classes of WIMP final states, namely $W^+ W^-$ and 95% $b bar{b}$ + 5% $tau^+tau^-$. Conversely, if WIMP properties were to be learned from production in future accelerators, then the flavor ratios of $agt$ GeV solar neutrinos might be useful for inferring $theta_{13}$ and the mass hierarchy.
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