You are getting married and your dearest relative has baked you a cake which fills the volume between the two planes, $z=0$ and $z=3x + 6y + c$, and inside the cylinder $x^2 + y^2 = 1$. You are to cut it in half by making two vertical slices from the center outward. Suppose one of the slices is at $\theta = 0$ and the other is at $\theta = \psi$.

What is the limit, $\displaystyle \lim_{c \rightarrow \infty} \psi$?