$$\left\{ 1-\dfrac{2}{3}:\left[ \dfrac{3}{7}:\left( \dfrac{3}{14}+\dfrac{3}{4}\right) +\dfrac{1}{4}\right] \right\} :\left[ 1-\dfrac{3}{4}\left( 1-\dfrac{1}{4}\right) \left( \dfrac{1}{3}+\dfrac{1}{5}\right) \right] +\dfrac{1}{7}=$$

$$\left\{ 1-\dfrac{2}{3}:\left[ \dfrac{3}{7}:\left( \dfrac{6+21}{28}\right) +\dfrac{1}{4}\right] \right\} :\left[ 1-\dfrac{3}{4}\cdot \left( \dfrac{4-1}{4}\right) \left( \dfrac{5+3}{15}\right) \right] +\dfrac{1}{7}=$$

$$\left\{ 1-\dfrac{2}{3}:\left[ \dfrac{\cancelto{1}{3}}{\cancelto{1}{7}}\cdot \dfrac{\cancelto{4}{28}}{\cancelto{9}{27}}+\dfrac{1}{4}\right] \right\} :\left[ 1-\dfrac{3}{\cancelto{2}{4}}\cdot \dfrac{\cancelto{1}{3}}{\cancelto{1}{4}}\cdot\dfrac{\cancelto{\cancelto{1}{2}}{8}}{\cancelto{3}{55}}\right] +\dfrac{1}{7}=$$

$$\left\{ 1-\dfrac{2}{3}:\left[ \dfrac{4}{9}+\dfrac{1}{4}\right] \right\} :\left[ 1-\dfrac{3}{10}\right] +\dfrac{1}{7}=$$

$$\left\{ 1-\dfrac{2}{3}:\left[ \dfrac{16+9}{36}\right] \right\} :\left[ \dfrac{10-3}{10}\right] -\dfrac{11}{7}=$$

$$\left\{ 1-\dfrac{2}{\cancelto{1}{3}}\cdot \dfrac{\cancelto{12}{36}}{25}\right\} :\dfrac{7}{10}+\dfrac{1}{7}=$$

$$\left\{ 1-\dfrac{24}{25}\right\} :\dfrac{7}{10}+\dfrac{1}{7}=$$

$$\left\{\dfrac{25-24}{25}\right\} :\dfrac{7}{10}+\dfrac{1}{7}=$$

$$\dfrac{1}{\cancelto{5}{25}}\cdot \dfrac{\cancelto{2}{10}}{7}+\dfrac{1}{7}=$$

$$\dfrac{2}{35}+\dfrac{1}{7}=$$

$$\dfrac{2+5}{35}=$$

$$\dfrac{7}{35}=$$

$$\dfrac{1}{5}$$