Hyperbola

Let the latus rectum of the hyperbola \(\frac{x^2}{9}-\frac{y^2}{b^2}=1\) subtend an angle of \(\frac{\pi}{3}\) at the centre of the hyperbola. If \(\mathrm{b}^2\) is equal to \(\frac{l}{\mathrm{~m}}(1+\sqrt{\mathrm{n}})\), where \(l\) and \(\mathrm{m}\) are co-prime numbers, then \(\mathrm{l}^2+\mathrm{m}^2+\mathrm{n}^2\) is equal to ________.