For the 2+1 dimensional three-wave equation, by using the known nonlinear constraints from 2+1 dimensions to 1+1 dimensions, we reduce it further to 0+1 dimensional (finite dimensional) Hamiltonian systems with constraints of Neumann type. These Hamiltonian systems are proved to be Liouville integrable by finding a full set of involutive conserved integrals and proving their functional independence. Moreover, almost-periodic solutions of the 2+1 dimensional three-wave equation are obtained by solving these Hamiltonian systems explicitly.

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