Long exact sequences of homology theories

Exercise 3.1.3 (Long exact sequences of homology theories). Use the coPuppe sequence of Lemma 2.4.28 to show that every homology theory gives rise to a long exact sequence \[ \cdots \to \widetilde E_{n+1}(Z) \xrightarrow {\partial } \widetilde E_n(X) \xrightarrow {f_*} \widetilde E_n(Y) \xrightarrow {g_*} \widetilde E_n(Z) \xrightarrow {\partial } \widetilde E_{n-1}(X) \to \cdots . \] Formulate and prove the analogous statement for cohomology theories.