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If a unit vector $\vec{a}$ makes angles $\pi/3$ with $\hat{i}$, $\pi/4$ with $\hat{j}$ and $\theta \in (0, \pi)$ with $\hat{k}$, then a value of $\theta$ is:
(1) $\frac{5\pi}{6}$
(2) $\frac{\pi}{4}$
(3) $\frac{5\pi}{12}$
(4) $\frac{2\pi}{3}$
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