Can you find out where I am going wrong?

and therefore

When it gets substituted in it produces

due to the trigonometric identity of

it becomes

when multiplied out this goes to

when this is integrated it becomes

therefore the area should be

Which then gets to (almost there, I promise)

and because sin(0) is 0 I left the second half out.

at last

I believe that I went wrong when I insert the values but I don't know how to change them