Given $\csc\theta=-\frac53$ and $\pi<\theta<\frac32\pi$, evaluate sine ,cosine, and tangent of $2\theta$ If $\csc\theta=\frac{-5}{3}$, what is the exact value of $\tan(2\theta)$, $\sin(2\theta)$, and $\cos(2\theta)$ on the interval of $\left(\pi, \frac{3\pi}{2}\right)$?
I think I'm getting the fraction negatives wrong. I've used the sine formula($2\sin{\theta}\cos{\theta}$), the cosine formula ($2\cos^2{\theta}-1$) and the tangent formula, $\left(\frac{\sin(2\theta)}{\cos(2\theta)}\right)$
originally answering the problem I got $\sin(2\theta)=\frac{24}{25}$,
 $\cos(2\theta)=\frac{7}{25}$, and $\tan(2\theta)=\frac{24}{7}$

$\csc \theta=-\frac{5}{3}$
$\implies \sin^2\theta=\frac{9}{25}$
$\implies \cos^2\theta=\frac{16}{25}$
$\implies \cos2\theta=2*\frac{16}{25}-1=\frac{7}{25}$
Also,
$\sin^22\theta=4\sin^2\theta\cos^2\theta=\frac{4\times9\times16}{25\times25}$
$\implies \sin2\theta=\frac{24}{25}$
That gives 
$\tan2\theta=\frac{24}{7}$
