L{sin^{2}2t} <------ This was the question

sin^{2}A = 1/2(1-cos2A) <------ this was a note on the question

Below is me trying to laplace it

1/2(1-cos2(2t))

1/2(1-cos4t)

1/2 * 1 - 1/2 cos4t

L 1/2 {1} - L 1/2 {s }

..........s ............s^{2}+32

1- ....... s .

2s .....2s^{2}+32

as you can see something doesn't seem correct and the answer doesn't flow like the other questions did so im not sure where im going wrong and help would be appreciated.

post looks like a bit of a mess because im not sure how to put in spaces. please ignore the(.)