The technique described by GP kind of does, but you don't have to get the first part of the maneuver perfect - it just reduces your angle relative to the parking spot. The backward driving then then fixes bad alignment and having a non-0 angle (but with limited space you might need iterate using back-and-forth moves).

Also, for OP: You'll often find that getting into a spot is difficult, but getting out again is trivial. Obviously you could try to just reverse the "leaving movement" as part of your parking maneuver. This can help with finding the perfect spot for starting the parking maneuver.