How do i combine two 2D matrices in one 3D matrix, where each 3D pixel represents the sum of two elements.

I am trying to create a 3D matrix that calculates all of the elements the following equation:

x*cos(theta)+y*sin(theta)

I have vectors of x, y, cos, & sin and also a 2D matrices of the two terms before addition. My question is how can I create a 3d matrix that contains all of the possible combinations for my four vectors. It should be a 3D matrix because the thetas are the same.

edit: the goal is to do this without using a for loop