In d) you are given that
$\displaystyle \displaystyle{\vec{T} = \frac{d\vec{L}}{dt}}$
Now, the angular momentum $\displaystyle \vec{L}$ points along the shaft of the spinning top, right? What you have found via the torque vector $\displaystyle \vec{T}$ is how the angular momentum is changing with time. I think you can get the angular component of how $\displaystyle \vec{L}$ changes with respect to time. Then all you need to do is sum it up so that it goes around once (1 period). It'll be good to see your numbers and calculations.