We construct a nonlinear sigma (NLσ) model description of 2+1d spin systems, by coupling together antiferromagnetic spin chains via interchain exchange terms. Our mapping incorporates methods developed recently by ourselves and by Senthil and Fisher, which aim at describing competition between antiferromagnetic and valence-bond-solid orders in quantum magnets. The resulting 2+1d O(4) NLσ model contains a topological θ-term whose vacuum angle θ varies continuously with δ, the bond-alternation

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... ength of the interchain interaction. This implies that the θ-vacua structure for this NLσ model can be explored by tuning δ in a suitable 2d spin system, which is strongly reminiscent of the situation for 1+1 AF spin chains with bond-alternation.