4\frac{2}{7}:1\frac{5}{21}+(4\frac{3}{13}\cdot\frac{14}{15}-3\frac{1}{3})-\frac{1}{13}.

Выполним действия по порядку.

1. $$4\frac{2}{7}:1\frac{5}{21}=\frac{4\cdot7+2}{7}:\frac{1\cdot21+5}{21}=\frac{30}{7}:\frac{26}{21}=\frac{30}{7}\cdot\frac{21}{26}=\frac{30\cdot21}{7\cdot26}=\frac{30\cdot3}{26}=\frac{15\cdot3}{13}=\frac{45}{13}=3\frac{6}{13}$$
2. $$4\frac{3}{13}\cdot\frac{14}{15}=\frac{4\cdot13+3}{13}\cdot\frac{14}{15}=\frac{55}{13}\cdot\frac{14}{15}=\frac{55\cdot14}{13\cdot15}=\frac{11\cdot14}{13\cdot3}=\frac{154}{39}=3\frac{37}{39}$$
3. $$3\frac{37}{39}-3\frac{1}{3}=3\frac{37}{39}-3\frac{1\cdot13}{3\cdot13}=3\frac{37}{39}-3\frac{13}{39}=\frac{37-13}{39}=\frac{24}{39}=\frac{8}{13}$$
4. $$3\frac{6}{13}+\frac{8}{13}=\frac{3\cdot13+6}{13}+\frac{8}{13}=\frac{39+6}{13}+\frac{8}{13}=\frac{45}{13}+\frac{8}{13}=\frac{45+8}{13}=\frac{53}{13}$$
5. $$\frac{53}{13}-\frac{1}{13}=\frac{53-1}{13}=\frac{52}{13}=4$$

Ответ: 4