In what circumstances will a defendant waive his Miranda right?

^2. Defendant also argues he "was not asked if he actually waived his rights." He does not follow up on this argument in any meaningful way. In any event, defendant did waive his rights. "[A] valid waiver of Miranda rights may be express or implied. [Citations.] A suspect's expressed willingness to answer questions after acknowledging an understanding of his or her Miranda rights has itself been held sufficient to constitute an implied waiver of such rights." (People v. Cruz (2008) 44 Cal.4th 636, 667.) That is precisely what happened here.