+128473 cot^2(75°)
Note..... csc^2(75°) = 1 + cot^2(75°) → csc^2(75°) - 1 = cot^2(75°)
sin(75°) = sin(30 + 45) = sin30cos45 + sin45cos30 =
(1/2) * sqrt(2)/2 + sqrt (2)/2 * sqrt (3)/2 =
sqrt (2) / 4 + sqrt (6) / 4
sin^2(75°) = [sqrt (2) / 4 + sqrt (6) / 4] = 2/16 + 2sqrt(12)/16 + 6/16 =
1/2 + sqrt(12)/8 = (1/2 + 2sqrt(3) / 8 ) = 1/2 + sqrt(3)/4 = [2 + sqrt(3)] / 4
1 / sin^2(75°) = 1 / [ (2 + sqrt(3) ) / 4] = 4 / [ 2 + sqrt(3)] =
[4 * (2 - sqrt(3)) ] / ( 2 + sqrt(3) * (2 - sqrt(3) ] =
[4 * (2 - sqrt(3)) ] / [ 4 - 3 ] =
8 - 4sqrt (3) = csc^2(75°)
csc^2(75°) - 1 = cot^2(75°)
8 - 4sqrt (3) - 1 = cot^2(75°)
7 - 4sqrt (3) = cot^2(75°)
