Trig equation (and its solutions)

(Should be) simple trigonometric equation: .

Given solutions [1] , [2a] , [2b]

Why is it, that with 'sum (difference) theorem' , I get different solutions than with (at least it seems so) (Headbang)

This is what I did:



or

Now we have two equations to solve:





and

I would do it this way except I don't get the solutions you noted down. I think I did it right...... :s