19. As shown in the figure, $A$, $B$, $C$, $D$ are the four interior angles of quadrilateral $ABCD$.\\
(1) Prove: $\tan \frac { A } { 2 } = \frac { 1 - \cos A } { \sin A }$;\\
(2) If $A + C = 180 ^ { \circ }$, $AB = 6$, $BC = 3$, $CD = 4$, $AD = 5$, find the value of $\tan \frac { A } { 2 } + \tan \frac { B } { 2 } + \tan \frac { C } { 2 } + \tan \frac { D } { 2 }$.\\
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