Let \( E : \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1,\, a > b \) and \( H : \frac{x^{2}}{A^{2}} - \frac{y^{2}}{B^{2}} = 1 \). Let the distance between the foci of \( E \) and the foci of \( H \) be \( 2\sqrt{3} \). If \( a - A = 2 \), and the ratio of the eccentricities of \( E \) and \( H \) is \( \frac{1}{3} \), then the sum of the lengths of their latus rectums is equal to:
