# A := latitude.
# B := longitude
# T := theta

> zB := <<cos(B),sin(B),0>|<-sin(B),cos(B),0>|<0,0,1>>;  zmB := simplify(MI(zB));

                      [cos(B)    -sin(B)    0]
                 zB = [sin(B)     cos(B)    0]
                      [  0          0       1]

		      [ cos(B)    sin(B)    0]
	        zmB = [-sin(B)    cos(B)    0]
		      [   0         0       1]

> xT := <<1,0,0>|<0,cT,sT>|<0,-sT,cT>>;

			 [1    0      0 ]
		    xT = [0    cT    -sT]
			 [0    sT     cT]

> yA := <<cos(A),0,-sin(A)>|<0,1,0>|<sin(A),0,cos(A)>>;  ymA := simplify(MI(yA));

                      [ cos(A)    0    sin(A)]
                 yA = [   0       1      0   ]
                      [-sin(A)    0    cos(A)]

		      [cos(A)    0    -sin(A)]
		ymA = [  0       1       0   ]
		      [sin(A)    0     cos(A)]

> rotTatAB := zB . yA . xT . ymA . zmB ;
 rotTatAB =

    [              2
    [(cos(B) cos(A)  + (sin(B) sT + cos(B) sin(A) cT) sin(A)) cos(B)

     - (-sin(B) cT + cos(B) sin(A) sT) sin(B) ,

                  2
    (cos(B) cos(A)  + (sin(B) sT + cos(B) sin(A) cT) sin(A)) sin(B)

     + (-sin(B) cT + cos(B) sin(A) sT) cos(B) ,

                                                                 ]
    -cos(B) cos(A) sin(A) + (sin(B) sT + cos(B) sin(A) cT) cos(A)]

    [              2
    [(sin(B) cos(A)  + (-cos(B) sT + sin(B) sin(A) cT) sin(A)) cos(B)

     - (cos(B) cT + sin(B) sin(A) sT) sin(B) ,

                  2
    (sin(B) cos(A)  + (-cos(B) sT + sin(B) sin(A) cT) sin(A)) sin(B)

     + (cos(B) cT + sin(B) sin(A) sT) cos(B) ,

                                                                  ]
    -sin(B) cos(A) sin(A) + (-cos(B) sT + sin(B) sin(A) cT) cos(A)]

    [
    [(-sin(A) cos(A) + cos(A) cT sin(A)) cos(B) - cos(A) sT sin(B) ,

    (-sin(A) cos(A) + cos(A) cT sin(A)) sin(B) + cos(A) sT cos(B) ,

          2         2   ]
    sin(A)  + cos(A)  cT]


> subrotTatAB := subs({cos(A) = cA,cos(B) = cB, sin(A) = sA, sin(B) = sB}, rotTatAB) ;

 subrotTatAB =

[                                                                                                          ]
[  2   2        2   2                      2                      2                                        ]
[cA  cB  - cT cA  cB  + cT       , sB cB cA  + sA sT - cB sB cT cA         , cA (-cB sA + sB sT + cB sA cT)]
[                                                                                                          ]
[                                                                                                          ]
[        2              2            2     2   2          2           2   2                                ]
[sB cB cA  - cB sB cT cA  - sA sT, cA  - cA  cB  + cT - cA  cT + cT cA  cB , -cA (sB sA + cB sT - sB sA cT)]
[                                                                                                          ]
[                                                                                                          ]
[                                                                              2            2              ]
[cA (-cB sA + cB sA cT - sB sT)  , cA (-sB sA + sB sA cT + cB sT)          , cA  cT + 1 - cA               ]
[                                                                                                          ]