已知3个球心角（A0、B0、C0）及球体半径R，计算：球面三角的角度(A、B、C)、球面三角的面积、以及球角锥的体积
（涉及角度均为弧度制）
1、计算球面三角形的边长a、b、c：
a = A0*R; （弧长=弧度*球半径）
b = B0*R;
c = C0*R;
2、计算球面角：
（1）方法一：基于余弦定理求解：
故，A = acos( (cosa-cosbcosc)/(sinbsinc))，同理可计算球面角B和C
（2）方法二，也可有正弦公式求得
3、计算球面超（spherical excess）：
E=A+B+C-Pi （球面三角的内角和减去普通三角的内角和）
球面超的另外一种算法：
其中，a、b、c为球面三角的边长，s为周长的一半（s = 0.5*(a+b+c)）。
4、球面三角面积：
S = E*R^2
5、球角锥体积：
V = S*R/3
#===================================
以三个直角的球面角特例进行验证计算
Matlab程序如下：
clc;clear
A0 = pi/2; B0 = pi/2; C0 = pi/2;
d = 1; % set diameter of sphere as 1.0
r=d/2;
a = A0*r; b = B0*r; c = C0*r;
s = (a+b+c)/2;
% The 1st method for calculation of Spherical Angle
cosA1 = (cos(a/r)-cos(b/r)*cos(c/r))/(sin(b/r)*sin(c/r));
A1 = acos(cosA1);
disp("Spherical Angle 1:");
disp(A1);
% The 2nd method for calculation of Spherical Angle
sinA2 = (sin((s-b)/r)*sin((s-c)/r)/sin(b/r)/sin(c/r))^0.5;
A2 = asin(sinA2)*2;
disp("Spherical Angle 2:");
disp(A2)
% The 1st method for the calculation of Spherical Excess
E1 = A1*3-pi;
disp("Spherical Excess 1:");
disp(E1);
% The 2nd method for the calculation of Spherical Excess
temp = tan(0.5*s/r) * tan(0.5*(s-a)/r) * tan(0.5*(s-b)/r) * tan(0.5*(s-c)/r);
temp = temp^0.5;
E2 =atan(temp)*4;
disp("Spherical Excess 2:");
disp(E2);
%Surface area of the Spherical Triangle:
SurfArea = E2*r^2;
disp("Surface area of the Spherical Triangle:");
disp(SurfArea);
%Volume of the Spherical Pyramid
VsphPyramid = SurfArea*r/3;
disp("Volume of the Spherical Pyramid:");
disp(VsphPyramid);
注：上图中“球面积为4piR^2，其1/8应为piR2/2”。
参考资料：
1. https://mathworld.wolfram.com/SphericalTrigonometry.html
2. https://mathworld.wolfram.com/SphericalExcess.html
3. https://mathworld.wolfram.com/SphericalTriangle.html
4. https://baike.baidu.com/item/%E7%90%83%E9%9D%A2%E4%B8%89%E8%A7%92%E5%AD%A6/1307052?fr=aladdin