How to find vector coordinates given information of 2 vectors and corresponding angles

Question

I have the coordinates of 2 vectors, and the angles between each vector. I'm trying to form a tetrahedral shape, like the ones in the CH4 molecule. What would be the simplest way to go about doing this? My idea was to have a function with three inputs: The coordinates of the first vector, the second vector, and a 2d array where each element of the array contains the angle between one vector and another vector. For example the array might be [ [x, y, z], [x, a, b], [y, a, c], [z, b, c] ], as those would be the angles that correspond to the other vectors, in order of 1st, 2nd, 3rd, and 4th. I'm not sure if this makes complete sense, but I would also appreciate a simpler idea to solve this problem.