Solve the equation sin<sup>2</sup> x - sin x - 2 = 0, for x on the interval 0 ≤ x < 2π.
Step-by-step Solution:
Given that: \[ \sin^2 x - \sin x - 2 = 0 \] \[ \Rightarrow (\sin x - 2)(\sin x + 1) = 0 \] \[ \Rightarrow \sin x = -1 \] Hence: \[ x = \frac{3\pi}{2} \]