What's an efficient way to solve for the thetas here? Especially in the three-dimensional case, you end up with a rather nasty system of equations if you attempt to solve them by hand, and something less nasty but still very costly in terms of the number of trig functions, multiplications, and additions you have to do if you compute the angles geometrically using law of cosines, given a point that you want the end effector to be at.
What's an efficient way to solve for the thetas here? Especially in the three-dimensional case, you end up with a rather nasty system of equations if you attempt to solve them by hand, and something less nasty but still very costly in terms of the number of trig functions, multiplications, and additions you have to do if you compute the angles geometrically using law of cosines, given a point that you want the end effector to be at.