<s>[INST] Find the value of $\sin(2\theta)$ when $\cot(\theta) + \tan(\theta) = 2.5 $ I have an homework question that goes like:
$\cot(\theta) + \tan(\theta) = 2.5 $ is valid on some angles $\theta$ at section $0 < \theta < \pi/2$.
Find the value of $\sin(2\theta)$. (There is no need to find the value of $\theta$ in order to get the answer).
(a) $0.4 \quad$ (b) $0.5 \quad$ (c) $0.6 \quad$ (d) $0.7 \quad$ (e) $0.8$
An explanation on how to get the correct answer will be helpful.
 [/INST] \begin{align*}
     \cot \theta+\tan \theta
  &= \frac{\cos \theta}{\sin \theta}+\frac{\sin \theta}{\cos \theta} \\
  &= \frac{\cos^{2} \theta+\sin^{2} \theta}{\sin \theta \cos \theta} \\
  &= \frac{1}{\sin \theta \cos \theta} \\
  &= \frac{2}{\sin 2\theta}
\end{align*}
</s>