I'd argue that Machiavelli didn't really believe much of what was written in The Prince. First, Machiavelli, aside from in The Prince, was a very consistent supporter of republican government (contrast, eg his Discourses on Livy); also, he held several high offices in the Republic, and was fired, tortured, and sentenced to house arrest following the Medici return to power. Second off, much of his advice given in The Prince was objectively terrible, and would have increased the likelihood of a counter-counter-coup against the Medici- Mary Dietz gives a longer argument here (HT Gwern), which Wikipedia summarizes as:

• He discourages liberality and favors niggardliness to guarantee support from the people. Yet Machiavelli is keenly aware of the fact that an earlier pro-republican coup had been thwarted by the people's inaction that itself stemmed from the prince's liberality.
• He supports arming the people despite the fact that he knows the Florentines are decidedly pro-democratic and would oppose the prince
• He encourages the prince to live in the city he conquers. This opposes the Medicis' habitual policy of living outside the city. It also makes it easier for rebels or a civilian militia to attack and overthrow the prince.

(Even if it wasn't a trap, it's likely Machiavelli had severely compromised his own principles and ideas in The Prince in order to gain favor with the Medici.)