I'm attempting to create a series of angles in a section of 1/2" copper pipe. The goal here isn't to bend the pipe into an actual curve, but rather to create short sections that butt up against one another at angles. The eventual goal is a dragonfly tail (two of them, actually), as in this image:

(Those are technically damselflies, but you get the idea.)
My initial thought was to cut the pipe at an angle at each section (using half the angle I need), rotate one piece 180 degrees so that the oval ends line back up at the full angle, and then solder them back together. The first part of that was easy, but joining them back up is proving to be challenging - I've managed to dribble a lot of solder onto the firebrick, but haven't been able to get the pieces to stick.
Any suggestions? I'm not sure whether I just need more soldering practice/better technique, or whether I'm barking up the wrong tree with my whole approach. I did consider using sweat fittings, but I need some angles other than 45 and 90 degrees.
I don't actually care if the join seams are visible - I can incorporate that into the visual design. Nor do I need a great deal of structural integrity beyond the simple ability to hold its own weight when suspended from a string. The wings will be made of wire, so there shouldn't be a huge amount wind stress to worry about.