Explanation

The options show this is the standard problem 8sinθ − 4sin²θ (the stored 'sin2θ' is a transcription of sin²θ). Completing the square: 8sinθ − 4sin²θ = 4 − 4(sinθ−1)² ≤ 4, with equality when sinθ = 1. Hence the maximum value is 4 — option B. (As literally printed, with sin 2θ, the maximum would be 6√3, which is not among the options, confirming the transcription reading.)