The value of sin(180 - theta/2) can be derived using trigonometric identities, specifically sin(A - B) = sin A cos B - cos A sin B. Since sin(180) equals 0 and cos(180) equals -1, the expression simplifies significantly. To express sin(180 - theta/2) in terms of theta, one can also utilize the identity for sin(theta/2), which is ±√((1/2)(1 - cos(theta))). The discussion emphasizes the importance of clarifying the desired output, whether it be a numerical value or a function of theta. Overall, the conversation highlights key trigonometric principles necessary for solving the problem.