$\cos \theta = \sqrt {1 - {{\sin }^2}\theta } = \sqrt {1 - {{\left( {\frac{{12}}{{13}}} \right)}^2}} = \frac{5}{{13}}$
and $\cos \phi = \frac{{ - 3}}{5},\sin \phi = \sqrt {1 - \frac{9}{{25}}} = \frac{{ - 4}}{5}$,
$\left[ \because {\pi < \phi < \frac{{3\pi }}{2}} \right]$
Now, $\sin (\theta + \phi ) = \sin \theta .\cos \phi + \cos \theta .\sin \phi $
$ = \left( {\frac{{12}}{{13}}} \right)\,\left( {\frac{{ - 3}}{5}} \right) + \left( {\frac{5}{{13}}} \right)\,\left( {\frac{{ - 4}}{5}} \right)$
$= \frac{{ - 36}}{{65}} - \frac{{20}}{{65}}$$ = \frac{{ - 56}}{{65}}$.
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