**Решение:**
1) \(4\frac{1}{5} \cdot \frac{7}{15} \cdot \frac{1}{3} = \frac{21}{5} \cdot \frac{7}{15} \cdot \frac{1}{3} = \frac{21 \cdot 7 \cdot 1}{5 \cdot 15 \cdot 3} = \frac{7 \cdot 7 \cdot 1}{5 \cdot 5 \cdot 3} = \frac{49}{75}\)
2) \(4\frac{1}{5} : (\frac{7}{15} : \frac{1}{3}) = \frac{21}{5} : (\frac{7}{15} \cdot \frac{3}{1}) = \frac{21}{5} : \frac{7 \cdot 3}{15} = \frac{21}{5} : \frac{7}{5} = \frac{21}{5} \cdot \frac{5}{7} = \frac{21 \cdot 5}{5 \cdot 7} = 3\)
3) \((5\frac{8}{9} : 1\frac{17}{36}) : 4\frac{1}{5} = (\frac{53}{9} : \frac{53}{36}) : \frac{21}{5} = (\frac{53}{9} \cdot \frac{36}{53}) : \frac{21}{5} = \frac{36}{9} : \frac{21}{5} = 4 : \frac{21}{5} = 4 \cdot \frac{5}{21} = \frac{20}{21}\)
4) \((2\frac{1}{4} + \frac{4}{6}) : 3\frac{2}{5} - \frac{3}{4} = (\frac{9}{4} + \frac{2}{3}) : \frac{17}{5} - \frac{3}{4} = (\frac{27 + 8}{12}) : \frac{17}{5} - \frac{3}{4} = \frac{35}{12} : \frac{17}{5} - \frac{3}{4} = \frac{35}{12} \cdot \frac{5}{17} - \frac{3}{4} = \frac{175}{204} - \frac{3}{4} = \frac{175}{204} - \frac{153}{204} = \frac{22}{204} = \frac{11}{102}\)
**Ответ:**
1) \(\frac{49}{75}\); 2) \(3\); 3) \(\frac{20}{21}\); 4) \(\frac{11}{102}\)