Answer
$sin~2\theta = 2~cos~\theta ~sin~\theta$
Work Step by Step
From Exercise 45:
$(cos~\theta+i~sin~\theta)^2 = cos~2\theta + i~sin~2\theta$
From Exercise 46:
$(cos~\theta+i~sin~\theta)^2 = cos^2~\theta - sin^2~\theta + 2i~cos~\theta ~sin~\theta$
We can equate the imaginary part of each expression:
$i~sin~2\theta = 2i~cos~\theta ~sin~\theta$
We can cancel $i$ form each side of the equation:
$sin~2\theta = 2~cos~\theta ~sin~\theta$