When you first strip the line of the reel and start fishing, it lands in tight spring-like coils at your feet. After an hour or two, the line has relaxed a bit, making it much easier to handle and less likely to tangle.
The answer: tuck the rod under your arm and give the line a bit of a stretch. Starting at one end, take hold of a yard or so of line between your hands and give it a gentle tug, feeling the natural stretch in the line. Move the line along and do the same with the next yard, and the next, until you reach the end. Look down at your feet, and there's the line lying in gentle curves, not those tight coils. Now there's no excuse for not making the perfect cast!
Another tip Ian gave me: that stretch is the mark of a healthy fly line. When it loses its stretch, it's time to buy a new one.
Ian's advice reminded me why I still visit my local gun & tackle shop, rather than scrabbling round the internet for the lowest possible price.