Answer
$-\frac{4}{5}$
Work Step by Step
1. $f(2\theta)=sin(2\theta)=2sin\theta cos\theta$
2. Use the given figures, we have $sin\theta=\frac{2}{\sqrt 5}, cos\theta=-\frac{1}{\sqrt 5}$
3. $f(2\theta)=2(\frac{2}{\sqrt 5})(-\frac{1}{\sqrt 5})=-\frac{4}{5}$
