$\frac{\sin \left(-660°\right)\tan \left(1050°\right)\sec \left(-420°\right)}{\cos \left(225°\right)\cos ec\left(315°\right)\cos \left(570°\right)}=$

$=\frac{(-)\sin \left(360°+300°\right)\tan \left(3\times 360°-30°\right)\sec \left(360°+60°\right)}{\cos \left(180°+45°\right)\text{cosec}\left(360°-45°\right)\cos \left(360°+210°\right)}$

$=\frac{(-)\sin 300°\times (-)\tan 30°\times \sec 60°}{(-)\cos 45°\times (-)\text{cosec}45°\times \cos 210°}$

$=\frac{\sin 60°\times (-)\tan 30°\times \sec 60°}{(-)\cos 45°\times (-)\text{cosec}45°\times (-)\cos 30°}$

$=\frac{\frac{\sqrt{3}}{2}\times (-)\frac{1}{\sqrt{3}}\times 2}{\frac{1}{\sqrt{2}}\times \sqrt{2}\times (-)\frac{\sqrt{3}}{2}}$

$=\frac{(-)1}{\left(-\frac{\sqrt{3}}{2}\right)}$

$=\frac{2}{\sqrt{3}}$