Given that the integers $a,b$ satisfy the equation $$[\frac{\frac{1}{a}}{\frac{1}{a}-\frac{1}{b}}-\frac{\frac{1}{b}}{\frac{1}{a}+\frac{1}{b}}]\left(\frac{1}{a}-\frac{1}{b}\right)\cdot \frac{1}{\frac{1}{a^2}+\frac{1}{b^2}}=\frac{2}{3},$$find the value of $a+b.$