Final answer:
The solutions to cos(theta) = -1/2 where 0 < theta < 2pi are theta = 2pi/3 and theta = 4pi/3.
Step-by-step explanation:
The solutions to the equation cos(theta) = -1/2 where 0 < theta < 2pi can be found by considering the unit circle. Since cos(theta) = -1/2, we know that the angle theta must be in the second or third quadrant. In the second quadrant, it forms a right triangle where the adjacent side is negative and the hypotenuse is positive. In the third quadrant, both the adjacent and hypotenuse sides are negative. Using the relationship between the cosine function and the coordinates on the unit circle, we can find two solutions for theta: theta = 2pi/3 and theta = 4pi/3.