I have another question =)

First I'll attach the image so that it's easier to follow:

For part a) I tried getting to the required answer but haven't been able to. I'll write down what I've done. Could someone tell me where I've gone wrong?

First I isolated t

so from x=2sint ===> t = arcsin(x/2)

then to get a cartesian equation, I've put t back into the y equation:

y=ln(sec(arcsin(x/2)))

which simplifies to y=ln(2/√(4-x^2))

differentiating i get:

(here im not sure if its right)

dy/dx=-x

then when t = pi/3

x=√3

y=ln2

so y - ln2=-√3 (x-√3)

when y=0

√3.x=3 + ln2

so x= 1/√3 . (3 + ln2)

but that isn't the answer....