Answer
$\dfrac{- 3}{5}$
Work Step by Step
We have:
$\sin \theta=\dfrac{2}{\sqrt 5}$ and $\cos \theta=-\dfrac{1}{\sqrt 5}$
We plug these values into the following identity:
$\cos (2 \ \theta)=\cos^2 \theta -\sin^2 \theta = (\dfrac{-1}{\sqrt 5})^2 -(\dfrac{2}{\sqrt 5})^2=\dfrac{- 3}{5}$