Let $M$ and $m$ respectively be the maximum and minimum values of the function $f ( x ) = \tan ^ { - 1 } ( \sin x + \cos x )$ in $\left[ 0 , \frac { \pi } { 2 } \right]$. Then the value of $\tan ( M - m )$ is equal to:
(1) $2 - \sqrt { 3 }$
(2) $3 - 2 \sqrt { 2 }$
(3) $3 + 2 \sqrt { 2 }$
(4) $2 + \sqrt { 3 }$