Rather than cutting the segments square you can cut the angles as you go. To do this set the sled at the desired angle and tip the blade to the desired miter angle. In this case with 12 segs it is 15 degrees. The picture below shows the setup and the first angle has been cut.
The photo below shows the second cut. The sled has been turned to the same angle on the other side of zero and the board has been flipped. The advantage to doing it this way is you wont have to miter small pieces.
With this method the pattern will be larger if you use 12 segments. To make a smaller pattern use 24 segments using this same method and change the blade angle to 7.5 degrees.
The individual segments will look like the picture below.
From here you glue the segments in two half rings so they can be corrected. If you use this method the next step is here.