I forgot to send my attempt yesterday. Basically it seems I had interpreted your attempts similary as Alan.
I have shown two different ways to get the minimum of E(). The firstis using the partial derivatives as you had tried but seems not appropriate given the shape of your function. I added a 3D-plot of the function we wish to minimize for B=7 and you can see that we have no useable minimum where both derivatives are zero. So I also passed the addition of a condition which would guarantee we get a minumum and not a maximum. Angles2() is pretty much the same as Alan had showed - the difference being that here the guess values are not constant but assigned as parameters of the function. Idea was that you could adopt those guesses dependent on B later. I didn't do that as I guess with the function you provided the minimum will always be at alpha=pi and Phi=pi/2. Maybe you should check your formulas.
Unfortunalety current versions of Mathcad (14/15) can only save down to MC11 format. We would need someone who has installed MC11 as well to save in the needed 2001 format.
So I attach my file and also pdf prints of Alan's and my file for your information.
EDIT: Had this reply open and worked intermediate on something, so I am late as Alan already sent his file in 2001 format. I'll delete the pdf of his file.