The tangent vector to r(<em>t</em>) at any <em>t</em> in the domain is

At <em>t</em> = π/6, the tanget vector is

To get the unit tangent, normalize this vector by dividing it by its magnitude:

So the unit tangent at the given point is

To find this answer you need to find the area of the whole cake and divide it by 8. To find area of a circle, you need the formula (pi)*r^2. The radius is the diameter divided by two. Your final formula would be (pi)*8^2. This is approx. 201.06 in^2. Divide this number by 8, and you have your answer. I got 25.13 in^2.
To answer your question, it is shown in the image below