 Coupling of three angular momenta can be done in several ways, as explained in the article on Racah W-coefficients.Using the notation and techniques of that article, total angular momentum states that arise from coupling the angular momentum vectors formula_2, formula_3, formula_9, and formula_10 may be written as
Alternatively, one may first couple formula_2 and formula_9 to formula_14 and formula_3 and formula_10 to formula_17, before coupling formula_14 and formula_17 to formula_20