(1/(1+r+l)-1/(2+2r))EllipticPi(((3r+2l)(r+1))/(r+l+1)^2,arccos(1-(2l)/(sqrt2.+r+l)),(2+3r/l)/4)/sqrt l-.13827661910812976996 ,where r=(cbrt(108+12sqrt69)+cbrt(108-12sqrt69))/6,l=sqrt(3r^2-1)