What is the value of $$\frac{\left[\left(\frac{5}{7} of \frac{1}{12} \times \frac{1}{4} - \frac{1}{2} \times \frac{1}{8}\right) + \frac{5}{4} \times \frac{8}{15} - \frac{2}{3}\right]}{\frac{1}{2} \div \frac{1}{4} + \frac{1}{2}}$$

= $$\frac{\left[\left(\frac{5}{7} of \frac{1}{12} \times \frac{1}{4} - \frac{1}{2} \times \frac{1}{8}\right) + \frac{5}{4} \times \frac{8}{15} - \frac{2}{3}\right]}{\frac{1}{2} \div \frac{1}{4} + \frac{1}{2}}$$

= $$\frac{\left[\left(\frac{5}{84}\times\frac{1}{4}-\frac{1}{16}\right)+\frac{2}{3}-\frac{2}{3}\right]}{\frac{1}{2}\times\frac{4}{1}+\frac{1}{2}}$$

= $$\frac{\left[\left(\frac{5}{336}-\frac{1}{16}\right)\right]}{2+\frac{1}{2}}$$

= $$\frac{\left[\left(\frac{5}{336}-\frac{21}{336}\right)\right]}{\frac{5}{2}}$$

= $$\frac{\frac{-16}{336}}{\frac{5}{2}}$$

= $$\frac{-16}{336}\times\ \frac{2}{5}$$

= $$\frac{-1}{21}\times\ \frac{2}{5}$$

= $$\frac{-2}{105}$$