PT\(\Leftrightarrow\left[{}\begin{matrix}sin\left(x-\dfrac{\pi}{3}\right)=0\\sin\left(x-\dfrac{\pi}{3}\right)=1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}sin\left(x-\dfrac{\pi}{3}\right)=sin0\\sin\left(x-\dfrac{\pi}{3}\right)=sin\text{}\text{}\dfrac{\pi}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{\pi}{3}=k\pi\\x-\dfrac{\pi}{3}=\dfrac{\pi}{2}+k2\pi\end{matrix}\right.\)\(\left(k\in Z\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{3}+k\pi\\x=\dfrac{5\pi}{6}+k2\pi\end{matrix}\right.\)\(\left(k\in Z\right)\)
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