#include <stdio.h>
#include <gsl/gsl_errno.h>

#define PI 3.1415926535897932384626433832795028841971693993751058
#define Rs 1
#define M (0.5*Rs)
#define R0 (15*Rs)
#define f(r) ((1.0-Rs/((double)r)))
#define bmin (1.5*sqrt(3.0))
#define THETAERROR 100000