My way is more complex and time consuming than dv8's example.
Step one. Make your guides to map out the cneter of the document, horizontal and vertical. Use the path shape tool (U shortcut) and create two circles
from center. Use the path, not the filled shape option. Stay on the same selected pathway to add the inner ring to the outer one.
control click on the path and fill it with your first color. Name the layer and the path. If you don't name the layer you will lose it, not that you will really need it again, but it is a good habit to get into. Be sure to save this as a psd now. Talk about losing work if you don't!
Step two. Creare a middle ring the same way. Make sure you just barely overlap the outer ring. Change the color you want to fill it with. Control click and on a new layer fill in the new color. Name the path and the layer. SAVE, lol.
Step 3. Make inner ring the same way. Fill it name the new layer and new path. SAVE.
Step 4. Now you are going to copy merge those layers. Select the three layers. Hold down, ctl/cmd +alt/opt, and click E.
Step 5. Place the three originals in a group just to get them out of the way and to easily hide your orginal work and just use copies of the layers. Select the 3 layers and to group them, use ctl/cmd + G. Name the group orginal rings. Name the copy merged layer purple rings. Turn off the eye/visibilty of the group.
Step 6. Best method for this is simple straight lines made with the pen tool, but it is also easy to use the polygonal lasso. I just like to use the pen and make a saved path. So that is what I will describe. Be sure you have your center guides in place. You will have made these in the beginning. Click pen tool at center point, click in upper corner, complete path by clicking by clicking to finish the triangle. Name this path wedge.
Step 7. This is two steps in one as some of the above are. Activate the wedge path (ctl/cmd click on the path). Now choose mask at the bottom of the layer panel and this will give you the wedge shape for the purple. Next, make a copy of this and call it blue wedge.
Step 8. Make a layer adjustment, choose hue/sat. Click the box to make adjustment to previous layer.
Step 9. Use the colorize option check box and choose the hue and sat you would like to make the next wedge.