lf $\theta$ the angle between thetangents from $(-1,0)$ to the circle $x^{2}+y^{2}-5x+4y-2=0$ , then $\theta=$

The angle theta between tangents from a point (x1, y1) to a circle with radius r and center (h, k) satisfies sin(theta/2) = r/d, where d is the distance from the point to the center. Here, the center is (2.5, -2), the radius is sqrt(2.5^2 + (-2)^2 + 2) = sqrt(6.25 + 4 + 2) = sqrt(12.25) = 3.5, and the distance d from (-1, 0) to (2.5, -2) is sqrt((2.5 - (-1))^2 + (-2 - 0)^2) = sqrt(3.5^2 + 2^2) = sqrt(12.25 + 4) = sqrt(16.25). Using sin(theta/2) = 3.5/sqrt(16.25) leads to tan(theta/2) = 7/4, so theta = 2*tan^-1(7/4).