Here's a list of examples I've seen:
- What do you think happened?
- Who do you think has killed him?
- Who do you think he killed?
How does this structure what/who do you think... work? It seems a bit odd that you've got happened after think in the first example, has killed after think in the second. In third, who and what have got nothing to do with the first clause in the sentence but with the second. Can it be used in the past and in the future? "Who did you think (had) killed him? Who do you think will call him?"
Apparently it can appear in the middle of any question when someone asks an opinion. Is that so? Are there more structures like this?