Answer
$$\eqalign{
& {\text{amplitude: 2}} \cr
& {\text{period: }}\pi \cr} $$
Work Step by Step
$$\eqalign{
& f\left( \theta \right) = 2\sin 2\theta \cr
& {\text{The functions of the form }}y = A\sin \left( {B\left( {\theta - C} \right)} \right) + D{\text{ have a vertical}} \cr
& {\text{stretch }}\left( {{\text{or }}{\bf{amplitude}}} \right){\text{ of }}\left| A \right|,{\text{ and a period of }}\frac{{2\pi }}{{\left| B \right|}} \cr
& {\text{Therefore, rewriting the function }}f\left( \theta \right) = 2\sin 2\theta {\text{ we obtain}} \cr
& \underbrace {f\left( \theta \right) = 2\sin \left( {2\left( {\theta - 0} \right)} \right) + 0}_{y = A\sin \left( {B\left( {\theta - C} \right)} \right) + D} \cr
& A = 2,{\text{ }}B = 2,{\text{ }}C = 0,{\text{ }}D = 0 \cr
& {\text{The amplitude is: }}\left| A \right| = 2 \cr
& {\text{Period: }}\frac{{2\pi }}{{\left| B \right|}} = \frac{{2\pi }}{{\left| 2 \right|}} = \pi \cr
& \cr
& {\text{amplitude: 2}} \cr
& {\text{period: }}\pi \cr} $$
