A new class of variational wave functions describing many-body systems with spin-dependent correlations is used to study solid 3He. The idea of spin coherent states is used to construct a variational coherent-state wave function for solid 3He as an antisymmetrized Jastrow-Nosanov wave function that also contains spin-dependent correlations. We investigate this wave function by a variational Monte Carlo method. The addition of triplet (three-body) correlations produces a ground-state energy per particle that is a considerable improvement upon other variational results, but still appreciable discrepancies with the experiment remain. We speculate that such discrepancies point to a non-negligible effect of more-than-three-body correlations for both liquid and solid 3He.