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Given the complex numbers $a=10(\cos \frac{4}{3}\pi +\mathrm{i}\cdot \sin \frac{4}{3}\pi )$, $b=7(\cos {150}^{\circ }+\mathrm{i}\cdot \sin {150}^{\circ })$ and $c=5(\cos \frac{7}{4}\pi +\mathrm{i}\cdot \sin \frac{7}{4}\pi )$, evaluate $\frac{a\cdot b}{c}$.