Consider the hyperbola x²/100−y²/64=1 with foci at S and S₁, where S lies on the positive x-axis. Let P be a point on the hyperbola, in the first quadrant. Let ∠SPS₁=α, with α<π/2. The straight line passing through S and having the same slope as that of the tangent at P to the hyperbola intersects the straight line S₁P at P₁. Let δ be the distance of P from the straight line SP₁, and β=S₁P. Then the greatest integer less than or equal to (βδ/9)sin(α/2) is _____________.