One other sugestion: Since you will be adding tile and mostlikely a trim piece at the top as a border, cut your sheets of white ice (Home Depot material??) about a 1/2" less than the total height of the framing, and plan to set it up a 1/4" from the floor sheathing and down 1/4" from top of framing. This will allow you a little wiggle room to fit those corners good and tight. Also keep in mind that you need to cut those sheets from the back side so as to avoid any chipping.
Reason being; the teeth on circular saws circulate upwards, and with that in mind, if your cutting the material "good-side-up", you may risk chipiping the finished surface.
So make sure you cut your 22.5 degree angle "FIRST!!" then measure for the lenght and make that cut. And both cuts from the back side. Starting from the left and working around to the right:I would suggest making two sample pieces that have the angles on them, and bring them together at the outside corner first so they match perfectly. Once you have a perfect fit, hold in place the piece that sits on the left side and measure from the end to the angle to get the lenght for the left side piece. Then put the two sample pieces together again at the right side angle and hold the piece on the right and measure from the left angle to the right angle piece. This gives you the length for the center piece. Cutting the middle piece to the exact length will be your challenge for the day, since your making both cuts from the back side. Then finish your last piece on the right.Also keep in mind to use a clamped straight edge for making these cuts.
I'm assuming all this is "Sheet Material" based on the description of white ice. Besides, I don't think there is a species of white ice tree out there to make wainscotting panels...:jester: Be a bit brittle don't ya think!:wink: