This is particularly tricky set of trigonometric nonlinear equations. How do I go about solving it analytically relative to A,B,C and D?
$\sin(x)\sin(y) - \cos(z)\sin(w)\sin(y) - \cos(w)\sin(x)\sin(z) - \cos(x)\cos(y)\sin(w)\sin(z) = A $
$\cos(y)\sin(z) - \sin(w)\sin(x)\sin(z) + \cos(w)\cos(z)\sin(y) + \cos(x)\cos(z)\sin(y) + \cos(w)\cos(x)\cos(y)\sin(z) = B $
$\cos(x)\sin(w) - \sin(w)\sin(y)\sin(z) + \cos(w)\cos(y)\sin(x) + \cos(w)\cos(z)\sin(x) + \cos(x)\cos(y)\cos(z)\sin(w) = C $
$\arccos\left\{\frac{1}{2}\left(\cos(w)\cos(x) + \cos(y)\cos(z) - \cos(w)\sin(y)\sin(z) - \cos(x)\sin(y)\sin(z) - \cos(y)\sin(w)\sin(x) - \cos(z)\sin(w)\sin(x) + \cos(w)\cos(x)\cos(y)\cos(z) - 1\right)\right\} = D $