For the functions $$f(\theta) = \alpha \tan^2\theta + \beta \cot^2\theta$$, and $$g(\theta) = \alpha \sin^2\theta + \beta \cos^2\theta$$, $$\alpha > \beta > 0$$, let $$\min_{0 < \theta < \frac{\pi}{2}} f(\theta) = \max_{0 < \theta < \pi} g(\theta)$$. If the first term of a G.P. is $$\left(\frac{\alpha}{2\beta}\right)$$, its common ratio is $$\left(\frac{2\beta}{\alpha}\right)$$ and the sum of its first 10 terms is $$\frac{m}{n}$$, $$\gcd(m, n) = 1$$, then $$m + n$$ is equal to _______.