To solve this expression, we need to evaluate each individual trigonometric function at the given angle.

Tg^2(pi/6) = tan(pi/6)
tan(pi/6) = 1/√3
Therefore, tan(pi/6)^2 = (1/√3)^2 = 1/3

cos(-pi/3) = cos(pi/3)
cos(pi/3) = 1/2

sin(-pi/2) = sin(-90 degrees)
sin(-pi/2) = -1

Now we can substitute these values back into the expression.

1/3 - 1/2 - 1 = -2/3 - 1 = -5/3

Therefore, Tg^2(pi/6) - cos(-pi/3) + sin(-pi/2) = -5/3