right

assume the degree is theta, radius is R

distance/R = 1/cos(theta) + tan(theta) - 2 * theta + 5.71

derivative of the right side:
tan(theta) * (1 + sin(theta)) / cos(theta)
let it equal to zero
sin^2(theta) + sin(theta) = cos^2(theta)

therefore sin(theta) = 0.5
so the angle is 30 degree