For $0 < x < \pi$,
$$\frac { \sin x \cdot \cos x } { \sin x + \cos x } = \frac { \sin x - \cos x } { 2 }$$
What is the sum of the $\mathbf { x }$ values that satisfy the equality?
A) $\frac { \pi } { 2 }$
B) $\frac { 5 \pi } { 4 }$
C) $\frac { 7 \pi } { 4 }$
D) $\pi$
E) $2 \pi$