Answer
$\sqrt 2 \sin \theta+\sqrt 2 \cos \theta$
Work Step by Step
$a \sin B \theta+b \cos B \theta=\sqrt {a^2+b^2} \sin (B \theta+C)$
When $a=b$; $a^2+a^2 =4$
$ \implies a=b=\sqrt 2$
Now, $E=2 \sin ( \theta+\dfrac{\pi}{4}) =\sqrt 2 \sin \theta+\sqrt 2 \cos \theta$
