Consider the hyperbola $$\dfrac{x^2}{100} - \dfrac{y^2}{64} = 1$$ with foci at S and S$$_1$$, where S lies on the positive x-axis. Let P be a point on the hyperbola, in the first quadrant. Let $$\angle$$SPS$$_1 = \alpha$$, with $$\alpha < \dfrac{\pi}{2}$$. The straight line passing through the point S and having the same slope as that of the tangent at P to the hyperbola, intersects the straight line S$$_1$$P at P$$_1$$. Let $$\delta$$ be the distance of P from the straight line SP$$_1$$, and $$\beta = S_1P$$. Then the greatest integer less than or equal to $$\dfrac{\beta\delta}{9}\sin\dfrac{\alpha}{2}$$ is _______.