Given that
$$A ( \sin \theta + \cos \theta ) + B ( \cos \theta - \sin \theta ) \equiv 4 \sin \theta$$
find the values of the constants \(A\) and \(B\).
Hence find the exact value of
$$\int _ { 0 } ^ { \frac { 1 } { 4 } \pi } \frac { 4 \sin \theta } { \sin \theta + \cos \theta } \mathrm { d } \theta$$
giving your answer in the form \(a \pi - \ln b\).