+343 Two positive numbers \(p\) and \(q\) have the property that their sum is equal to their product. If their difference is \(7\), what is \(\frac{1}{\frac{1}{p^2}+\frac{1}{q^2}}\)? Your answer will be of the form \(\frac{a+b\sqrt{c}}{d}\), where \(a\) and \(b\) don't both share the same common factor with \(d\) and \(c\) has no square as a factor. Find \(a+b+c+d\)
