Somebody tell me this is OVERKILL. If you follow the directions there is no need to try and level every pier to each other. I just finished a 12 x 24 wrap around deck around a oval 18' pool end. Never used anything but a level and a tape measure and the 1/2" gap around the pool's edge is spot on all around and I had 2-3" of fall. I don't think it need to be made any more complicated by adding a transit. As far as right angles go just use the Pythagorean theorem
en.wikipedia.org/wiki/Pythagorean_theorem or if your not mathematically inclined use 3' 4' 5' or 6' 8' 10' to check squareness (where 3'4' or 6'8' are the legs and 5' or 10' is the hypotenuse).
Do follow the directions closely but no need to get OCD. Just my opinion.