Answer
$\dfrac{-6\sqrt{10}}{25}$
Work Step by Step
Let us consider $\tan \theta=\dfrac{4}{3}$
Since, $\sin \theta$ and $\cos \theta$ bot are negative in third quadrant. so, we have $\sin \theta=-\dfrac{4}{5}$ and $\cos \theta=-\dfrac{3}{5}$
Now, $\sin \phi=-\dfrac{\sqrt {10}}{10}$ and $\cos \phi=\dfrac{3}{\sqrt {10}}$
This gives: $\phi=\pi-\dfrac{\pi}{3}=\dfrac{2\pi}{3}$
Now, $\sin(\theta-\phi)=\sin \theta \cos \phi-\sin \phi \cos \theta$
This implies that
$\sin \theta \cos \phi-\sin \phi \cos \theta=(-\dfrac{3}{5})(\dfrac{3}{2})-(\dfrac{-1}{\sqrt{10}})(\dfrac{-3}{5})$
or, $=\dfrac{-6\sqrt{10}}{25}$
