No, you don't need AoA, you need the climb/descent angle, and weight. The angle is easily calculated from (true) airspeed and rate of climb or descent.
https://www.princeton.edu/~stengel/MAE331Lecture7.pdf
You may be misled by some textbooks that use alpha, rather than the more conventional gamma (or frankly just about any other greek letter!) to describe that angle, and thought it was referring to AoA. You might find it helps taking an hour or two to derive the equations from basic principles, which helps them make a lot more sense. Plenty of good textbooks will lead you by the hand through that - my copy's in the office and I'm at home (it being Saturday evening!) but IIRC Anderson's "Introduction to Flight" does this well and is presently a very popular book in many universities.
G