For some \( \theta \in \left(0, \frac{\pi}{2}\right) \), let the eccentricity and the length of the latus rectum of the hyperbola \( x^2 - y^2 \sec^2 \theta = 8 \) be \( e_1 \) and \( l_1 \), respectively, and let eccentricity and the length of the latus rectum of the ellipse \( x^2 \sec^2 \theta + y^2 = 6 \) be \( e_2 \) and \( l_2 \), respectively. If \( e_1^2 = e_2^2 \left(\sec^2 \theta + 1\right) \), then \( \left|\dfrac{l_1 l_2}{e_1 e_2}\right| \tan^2 \theta \) is equal to __________.
