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Trigonometry

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Difficult

Double Angle Tangent

TRIG-XCFBJK

If angle $\theta$ has a cosecant of $-\sqrt{10}$, and $\theta$ lies in Quadrant III, determine the tangent for angle $2\theta$.

A

$\cfrac{2}{3}$

B

$\cfrac{4}{3}$

C

$-\cfrac{4}{3}$

D

$-\cfrac{3}{4}$

E

$\cfrac{3}{4}$