The shadow measures not just the horizontal angle change of the sun, but also the vertical angle change of the sun. A very common way to measure time is to ref

The shadow measures not just the horizontal angle change of the sun, but also the vertical angle change of the sun. A very common way to measure time is to reference the horizontal angle change w.r.t. noon. In that case you need two moments where you measure the horizontal angle. Where, for the first moment, you need to measure two vertical angles (probably more) and deduce that the sun has reached its highest point. In this witchcraft, you still measure two vertical angles and two horizontal angles. You just split up when you take the vertical angles.