When visualising the problem you should see similar to an achery target.
Every second circle (or hoop section) coloured in. My equation calculates the area of each hoop (as the difference of the area of the outer part and inner part of each coloured circle) and summing them together to find total area. The area of the first hoop (the biggest hoop) is simply
then the next biggest
then the next biggest
and so on until you get to the end
Add all these guys together and you get
In the next line of my calculation I simply removed
as a common factor.
I arrived at the solution