1) $3\sin(x - \pi) - 2 = 0$
$\Leftrightarrow -3\sin(\pi - x) = 2$
$\Leftrightarrow \sin x =-\dfrac23$
$\Leftrightarrow\left[\begin{array}{l}x =\arcsin\left(-\dfrac23\right) + k2\pi\\x = \pi - \arcsin\left(-\dfrac23\right) + k2\pi\end{array}\right.\quad (k\in\Bbb Z)$
2) $2\sin\left(\dfrac{x}{3} -\dfrac{\pi}{2}\right) - 1 = 0$
$\Leftrightarrow - 2\sin\left(\dfrac{\pi}{2} -\dfrac{x}{3}\right)=1$
$\Leftrightarrow \cos\dfrac{x}{3} = -\dfrac12$
$\Leftrightarrow \dfrac{x}{3} = \pm \dfrac{2\pi}{3} + k2\pi$
$\Leftrightarrow x = \pm 2\pi + k6\pi\quad (k\in\Bbb Z)$
