Yeah, when you change angles, you have to keep the line tight. Regardless of angles, keeping the line tight is an important factor.
1. Get a good hookset. Don't have a belly in the fly line. Set hard enough, and straight up, not back (it's a lift). Set it twice for good measure if you want.
2. Keep the line tight. Thats the big rule nomatter what. I like to change angles on them while they're still fresh and fighting. That part of the fight might be 1 or 2 seconds for a small trout, or 10 minutes for a energetic steelhead, or anything in between. Once I get em coming my way, I try to lead them to somewhere were I can handle the landing aspect. For average sized fish, perhaps some slow water. For truly large fish, I look for a beach point.
3. When they're close, and you get that head up out of the water, don't stop! If you play your cards right thats the end of the fight. The head comes up, you can take them anywhere you want so long as you drag them fast. But if you stop pulling them, and let the head go under, they often have another run in em. And its those close distance runs that, for me, they sometimes break the line.
4. I usually grab leader and as quickly as possible slide my hand down to the fly. If you get ahold of the fly, they ain't goin nowhere and the line won't break. If the fly is in a more difficult location, it's more of a hassle.