While the Series 3 'Coming Soon...' trailer has been existent on YouTube for over a decade, there wouldn't be many fans that would know, apart from those who watched the episode on its original broadcast(s) that the trailer debuted after the sixth episode of Series 3, The Lazarus Experiment. This was because, before the days of uninterrupted luxury that we get now, Doctor Who in its then-traditional Spring schedule, was taken off the air for a week as the whole night was taken up by the Eurovision Song Contest. As a one-off a comprehensive trailer of the rest of the forthcoming episode was shown instead of a trailer for 42, followed by a caption saying 'Dr Who will return in two weeks...' - imagine how painful a wait that was.
Strangely, this was never done again. Series 4 featured a coming soon trailer for the remaining episodes online after the final episode before Eurovision was aired, despite suffering another one-week break.
You can thank my stringent recordings of the episodes at their original transmission for this, which I still own. Apologies for the low quality, but my 9-year-old self was unaware of the consequences that recording in EP mode to fit as many episodes on one disc as possible would have on its perceived quality a decade later.