Inside the interval $0 \leq x \leq \pi$, the curve $y = \sin\left(x + \frac{1}{3}\pi\right)\cos x$ has two stationary points.
(i)[2]
Find the derivative $\frac{dy}{dx}$.
(ii)[2]
By using the formula for $\cos(A + B)$, show that at the stationary points on the curve, $\cos\left(2x + \frac{1}{3}\pi\right) = 0$.
(iii)[3]
Hence determine the exact $x$-coordinates of the stationary points.
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