from part (i) ...
$s^2 = 2+4\sin^2{t}+4\sin{t}\cos{t}$
using double angle identities ...
$s^2 = 2 + 4\left[\dfrac{1-\cos(2t)}{2}\right] + 2\sin(2t)$
$s^2 = 4 - 2\left[\cos(2t)-\sin(2t)\right]$
$s^2 = 4 + \sqrt{2} \left[\cos(2t) \cdot \dfrac{\sqrt{2}}{2} - \sin(2t) \cdot \dfrac{\sqrt{2}}{2}\right]$
$s^2 = 4 + \sqrt{2} \left[\cos(2t) \cos\left(\dfrac{\pi}{4}\right) - \sin(2t) \cdot \sin\left(\dfrac{\pi}{4}\right) \right]$
$s^2 = 4 + \sqrt{2} \cos\left(2t + \dfrac{\pi}{4}\right)$