Preamble
A two qubit/spin-1/2 system can be represented as
$$|\psi\rangle=\alpha|\uparrow\uparrow\rangle+\beta|\uparrow\downarrow\rangle+\gamma|\downarrow\uparrow\rangle+\delta|\downarrow\downarrow\rangle=\begin{pmatrix}\alpha\\\beta\\\gamma\\\delta\end{pmatrix}$$ where $\alpha,\beta,\gamma,\delta$ are complex numbers such that $|\alpha|^2+|\beta|^2+|\gamma|^2+|\delta|^2=1\tag{1}$ is the normalization condition. For convenience we can choose $\alpha=a$ strictly real as the global phase does not matter. This means that to specify the state, we need 7 real parameters. The equation (1) represents then the surface of a 7D Bloch sphere.
My question concerns non-entangled states in that sphere. For a state to be non-entangled it has to be of the form
$$|\psi\rangle=(\epsilon|\uparrow\rangle+\zeta|\downarrow\rangle)\otimes(\eta|\uparrow\rangle+\theta|\downarrow\rangle)=\begin{pmatrix}\epsilon\eta\\\epsilon\theta\\\zeta\eta\\\zeta\theta\end{pmatrix}$$ where $\epsilon,\eta,\zeta,\theta$ are complex numbers, such that $$|\epsilon|^2+|\zeta|^2=1=|\eta|^2+|\theta|^2.\tag{2}$$
Question
Equation (2) represents some kind of lower dimensional spheres surfaces embedded in the 7-sphere of eq. (1). This seems ok, the 7D-surface of the non-entangled states is null as there are more entangled states than non-entangled states (see Are there more entangled states or non-entangled ones? ).
How is the 7D Bloch sphere divided with respect to this non-entangled boundary? Does this boundary cut the surface of the Bloch-sphere on two regions?