Risolvi la seguente espressione

$$\left[ 1-\left( 2-\dfrac{1}{3}\right) \cdot \left( \dfrac{1}{3}+\dfrac{5}{6}:\dfrac{15}{8}\right) :\dfrac{7}{3}\right] \cdot \dfrac{3}{2}+\dfrac{13}{45}:\left( \dfrac{2}{3}+\dfrac{1}{5}\right)=$$

$$\left[ 1-\left( \dfrac{6-1}{3}\right) \cdot \left( \dfrac{1}{3}+\dfrac{\cancelto{1}{5}}{\cancelto{3}{6}}\cdot \dfrac{\cancelto{4}{8}}{\cancelto{3}{15}}\right) \cdot \dfrac{3}{7}\right] \cdot \dfrac{3}{2}+\dfrac{13}{45}:\left( \dfrac{10+3}{15}\right)=$$

$$\left[ 1-\dfrac{5}{3}\cdot \left( \dfrac{1}{3}+\dfrac{4}{9}\right) \cdot \dfrac{3}{7}\right] \cdot \dfrac{3}{2}+\dfrac{\cancelto{1}{13}}{\cancelto{3}{45}}\cdot \dfrac{\cancelto{1}{15}}{\cancelto{1}{13}}=$$

$$ \left[ 1-\dfrac{5}{3}\cdot \left( \dfrac{3+4}{9}\right) \cdot \dfrac{3}{7}\right] \cdot \dfrac{3}{2}+\dfrac{1}{3}=$$

$$\left[ 1-\dfrac{5}{3}\cdot \dfrac{7}{9}\cdot \dfrac{3}{7}\right] \cdot \dfrac{3}{2}+\dfrac{1}{3}=$$

$$\left[ 1-\dfrac{5}{9}\right] \cdot \dfrac{3}{2}+\dfrac{1}{3}=$$

$$\left[ \dfrac{9-5}{9}\right] \cdot \dfrac{3}{2}+\dfrac{1}{3}=$$

$$\dfrac{\cancelto{2}{4}}{\cancelto{3}{9}}\cdot \dfrac{\cancelto{1}{3}}{\cancelto{1}{2}}+\dfrac{1}{3}=$$

$$\dfrac{2}{3}+\dfrac{1}{3}=$$

$$\dfrac{3}{3}=$$

$$1$$