We consider the propositional modal mu-calculus, a logic proposed by Kozen in 1983. In this logic two operators μ and v are present, which express the least and greatest fixpoints of monotone operators on sets. Bradfield in 1998 proved for any n the existence of a mu-calculus formula that requires n alternations of μ and v. In this paper we consider the particular case n = 3 and we exhibit a new formula requiring 3 alternations. Our proof is independent of the technique of Bradfield, and is based on a new kind of game on infinite trees.