function Apr21()


function z = F(x)
% Convention. Point(k) has longitude phi(k) and latitude theta(k). We
% fix Point(1) at the north pole phi(1)=0, theta(1) = pi/2, and force the
% longitude of Point(2) to be on the Greenwich meridian, phi(2) = 0;
% x will house theta(2), phi(3), theta(3), phi(4) and theta(4) in that
% order
phi = [0 0 x(2) x(4)];
theta = [pi/2 x(1) x(3) x(5)];
A_Red   = Area(phi(1),theta(1),phi(2),theta(2),phi(3),theta(3));
A_Green = Area(phi(1),theta(1),phi(2),theta(2),phi(4),theta(4));
A_Blue  = Area(phi(1),theta(1),phi(3),theta(3),phi(4),theta(4));
A_White = Area(phi(2),theta(2),phi(3),theta(3),phi(4),theta(4));
z = R*A_Red + G*A_Green + B*A_Blue + W*A_White;