I laid the stool legs out on an equilateral triangle.
Each leg has the same splay and rake (which might not make sense here). There are a couple of ways to lay out this pattern, both start with drawing a circle that defines where you want your stool legs to to enter the seat. You can see that circle above in the picture of my stool seat blank. I determined what looked good by following an article from Mike Dunbar in popular woodworking and by making a model.
The simplest way, in my opinion, to lay out the triangle is to drop a diameter through the circle using your compass prick point as a reference, then you set your compass to the radius of the circle and strike an arc using the intersection of the diameter and the circle edge as the pivot point. Then you connect the dots.
The other way is essentially the same approach, but you define the diameter using a right angle construction with your compass. First you use the center point of your circle to set the compass to the radius. Then you strike to intersecting lines from a random point on the circle edge. Next, set your compass to the distance between those two intersections and draw another arc. Connect the dots.
No matter which approach you use, you then draw diameters into the center of the circle to set you sight lines for the legs.
Then set your bevel and drill!!