Вычислите: 1) \(\left(2:3\frac{1}{5}+\left(3\frac{1}{4}:13\right)\cdot\frac{2}{3}+\left(2\frac{5}{18}-\frac{17}{36}\right)\cdot\frac{18}{65}\right)\cdot\frac{1}{3}\).

\[3\frac{1}{5}=\frac{16}{5},\qquad 3\frac{1}{4}=\frac{13}{4},\qquad 2\frac{5}{18}=\frac{41}{18}.\]

\[2:\frac{16}{5}=2\cdot\frac{5}{16}=\frac{5}{8}.\]

\[\left(\frac{13}{4}:13\right)\cdot\frac{2}{3}=\left(\frac{13}{4}\cdot\frac{1}{13}\right)\cdot\frac{2}{3}=\frac{1}{4}\cdot\frac{2}{3}=\frac{1}{6}.\]

\[\left(\frac{41}{18}-\frac{17}{36}\right)\cdot\frac{18}{65}=\left(\frac{82}{36}-\frac{17}{36}\right)\cdot\frac{18}{65}=\frac{65}{36}\cdot\frac{18}{65}=\frac{1}{2}.\]

\[\left(\frac{5}{8}+\frac{1}{6}+\frac{1}{2}\right)\cdot\frac{1}{3}=\left(\frac{15}{24}+\frac{4}{24}+\frac{12}{24}\right)\cdot\frac{1}{3}=\frac{31}{24}\cdot\frac{1}{3}=\frac{31}{72}.\]

Ответ: \(\frac{31}{72}\).