To solve the given equation, we can simplify both sides using trigonometric identities.

Given equation: 2sin(pi+t) + cos(pi/2 - t) = -1/2

Using the following trigonometric identities:
sin (pi + t) = -sin(t)
cos (pi/2 - t) = sin(t)

Now we substitute these identities into the equation:
2(-sin(t)) + sin(t) = -1/2
-2sin(t) + sin(t) = -1/2
-sin(t) = -1/2

Multiplying both sides by -1:
sin(t) = 1/2

Therefore, the solution to the equation is t = pi/6.