Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

The right side is $-2-(x-3{)}^2\le -2$, while the left side is at least -2 . Equality forces $x=3,\sin (\theta +\pi /3)=-1$. In $[0,4\pi ]$ this gives $\theta =7\pi /6,19\pi /6$, hence exactly two ordered pairs.