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ATC always takes priority over waypoints and this will happen during takeoffs and landings.
Just before taking off, ATC will probably give you a heading to fly. This may or may not be in the direction of your waypoint. She's telling you to fly that heading so you don't interfere with other inbound/outbound traffic at the airport. You should fly that heading until she tells you to resume your own navigation, at which time you can turn to your waypoint.
When you are inbound for landing, ATC will give you heading and altitude to follow. At this point, just forget all about waypoints and listen to ATC. Basically she's lining you up for a good approach and keeping you from running into other airport traffic. Just do what she tells you and she'll generally line you up pretty nicely with the runway.
Waypoints are what you fly when you're not within ATC's control. Hope this helps!