tan (-2pi / 3) = tan ( -120°) = tan (240°) = tan of a 60° angle in quadrant 3 = sqrt (3)
sin (7pi/4)
(7pi/4) - 2pi = (7pi/4 - 8pi/4) = -pi/4
sin (-pi/4) = - 1/sqrt (2)
sec (-pi) = sec (pi) = -1
So we have
sqrt (3) / ( -1/sqrt 2) - (-1) =
-sqrt (6) + 1