#include <complex.h>
#include <math.h>
typedef double _Complex C;
typedef double R;
C dilog(C);

static R const pi = 3.141592653589793238;
static C c(R x, R y){C a; __real__ a = x; __imag__ a = y; return a;}
static C w(C z){return z - 1/z;}
R Vol(R th[6]){C a[6]; {int j=6; while(j--) a[j] = cexp(c(0, th[j]));}
C a03 = a[0]*a[3], a14 = a[1]*a[4], a25 = a[2]*a[5];
C q0 = a03 + a14 + a25 + a03*a14*a25
       + a[0]*a[1]*a[5] + a[0]*a[2]*a[4] + a[1]*a[2]*a[3] + a[3]*a[4]*a[5],
q1 = - w(a[0])*w(a[3]) - w(a[1])*w(a[4]) - w(a[2])*w(a[5]),
q2 = 1/a03 + 1/a14 + 1/a25 + 1/(a03*a14*a25)
   + 1/(a[0]*a[1]*a[5]) + 1/(a[0]*a[2]*a[4])
   + 1/(a[1]*a[2]*a[3]) + 1/(a[3]*a[4]*a[5]);
C z = (-q1 + csqrt(q1*q1 - 4*q0*q2))/(2*q2);
R s = 0; {int j=6; while(j--) s += th[j];}
C ll = 0; {int j=3; while(j--) ll += clog(a[j])*clog(a[j+3]);}
C L = 0.5*(dilog(z)
     + dilog(a03*a14*z) + dilog(a03*a25*z) + dilog(a14*a25*z)
     - dilog(-z/(a[0]*a[1]*a[2])) - dilog(-z/(a[0]*a[4]*a[5])) - dilog(-z/(a[1]*a[3]*a[5]))
     - dilog(-z/(a[2]*a[3]*a[4])) + ll);
return -creal(L) + pi*(cimag(clog(-q2)) + 0.5*s) - 1.5*pi*pi;}

#include <stdio.h>
R a[6]; 
void s() {int y=6; while(y--) a[y] = pi/2;}
void sj(R b){int j=6; while(j--){s(); a[j] = b;
    printf("one dim ang, %d %e\n%20.15f\n%20.15f\n", j, b, pi*b/4, Vol(a));}}
int main(){
  s(); printf("%20.15f\n%20.15f\n", pi*pi/8, Vol(a));
  sj(1.); sj(1.5); sj(2.);
return 0;}

/*
   1.233700550136170
   1.233700550136168
one dim ang, 5 1.000000e+00
   0.785398163397448
   0.074716812240217
one dim ang, 4 1.000000e+00
   0.785398163397448
   0.074716812240219
one dim ang, 3 1.000000e+00
   0.785398163397448
   0.074716812240219
one dim ang, 2 1.000000e+00
   0.785398163397448
   0.074716812240219
one dim ang, 1 1.000000e+00
   0.785398163397448
   0.074716812240219
one dim ang, 0 1.000000e+00
   0.785398163397448
   0.074716812240219
one dim ang, 5 1.500000e+00
   1.178097245096172
   1.067022639087769
one dim ang, 4 1.500000e+00
   1.178097245096172
   1.067022639087769
one dim ang, 3 1.500000e+00
   1.178097245096172
   1.067022639087769
one dim ang, 2 1.500000e+00
   1.178097245096172
   1.067022639087769
one dim ang, 1 1.500000e+00
   1.178097245096172
   1.067022639087769
one dim ang, 0 1.500000e+00
   1.178097245096172
   1.067022639087769
one dim ang, 5 2.000000e+00
   1.570796326794897
   2.229864886519620
one dim ang, 4 2.000000e+00
   1.570796326794897
   2.229864886519620
one dim ang, 3 2.000000e+00
   1.570796326794897
   2.229864886519620
one dim ang, 2 2.000000e+00
   1.570796326794897
   2.229864886519620
one dim ang, 1 2.000000e+00
   1.570796326794897
   2.229864886519620
one dim ang, 0 2.000000e+00
   1.570796326794897
   2.229864886519620
*/