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If angle $\theta$ has a cosine of $\cfrac{\sqrt{2}}{3}$, and $\theta$ lies in Quadrant IV, determine the cotangent for angle $2\theta$.

A

$-\cfrac{5\sqrt2}{2}$

B

$\cfrac{5\sqrt7}{28}$

C

$\cfrac{5\sqrt{14}}{28}$

D

$-\cfrac{2\sqrt{14}}{7}$

E

$\cfrac{2\sqrt{14}}{5}$

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