$4\frac{2}{7}:1\frac{5}{21}+\left(4\frac{3}{13}\cdot\frac{14}{15}-3\frac{1}{3}\right)=\frac{30}{7}\cdot \frac{21}{26}+\left(\frac{55}{13}\cdot\frac{14}{15}-\frac{10}{3}\right)=$

$=\frac{15\cdot 3}{13}+\left(\frac{11\cdot 14}{13\cdot 3}-\frac{10}{3}\right)=\frac{45}{13}+\frac{154-130}{13\cdot 3}=\frac{45}{13}+\frac{8}{13}=\frac{53}{13}=4\frac{1}{13}$