Let T be a triangulated category with shift functor Σ T→T. Suppose (A,B) is a co-t-structure with coheart S=ΣA⊂B and extended coheart C=Σ2A⊂B=S∗ΣS, which is an extriangulated category. We show that there is a bijection between co-t-structures (A',B') in T such that A⊂A'⊂ΣA and complete cotorsion pairs in the extended coheart C. In the case that T is Hom-finite, k-linear and Krull-Schmidt, we show further that there is a bijection between complete cotorsion pairs in C and functorially finite torsion classes in mod S.