I am trying to solve this equation derived from matrix multiplication (where $a,b,c,d$ are constants):
$-a \cos(\theta) \sin(\alpha)-b\sin(\theta) \sin(\alpha)+c\cos(\theta)\cos(\alpha)+d\sin(\theta)\cos(\alpha) = 0$
The answer should be $\theta = (x_1+x_2)/2$ , $\alpha = (x_1-x_2)/2$ where $x_1 = \arctan((c-b)/(a+d))$ and $x_2 = \arctan((c+b)/(a-d))$
Here is what I have so far:
$\begin{align} a(-\sin(\theta+\alpha)+\sin(\theta-\alpha))&+b(\cos(\theta-\alpha)+\cos(\theta+\alpha))+c(-\cos(\theta-\alpha) \\&+ \cos(\theta+\alpha))+d(\sin(\theta+\alpha)+\sin(\theta-\alpha))=0 \end{align}$
I am stuck at this point though
Thanks