$c_1$ and $c_2$ are equal [@Elby-Bub].

We conclude by noting that the present treatment regarding the three-particle state (2) can be readily extended to $n$-particle states ($n \geq 3$) of the form $$|\Psi\rangle = c_1 |z_1\rangle |z_2\rangle \cdots |z_n\rangle + 
c_2 |-z_1\rangle |-z_2\rangle \cdots |-z_n\rangle  .$$ Indeed, by letting $|z_j\rangle^{\textstyle\ast}$ be $$|z_j\rangle^{\textstyle\ast} = \cos\frac{\vartheta_j}{2} e^{-iz_{j}\varphi_{j}/2}
|z_j\rangle + z_j \sin\frac{\vartheta_j}{2} e^{iz_{j}\varphi_{j}/2} |-z_j\rangle ,$$ with $j=N+1, N+2,\ldots,n,$ and $N=2,3,\ldots,\mbox{$n-1$},$ and projecting $|\Psi\rangle$ onto the direct product state $|z_{N+1}\rangle^{\textstyle\ast} |z_{N+2}\rangle^{\textstyle\ast} \cdots |z_{n}\rangle^{\textstyle\ast}$, one finds that the resulting $N$-particle state $|\Psi^{+}_{12 \cdots N} \rangle$, $$p^{1/2}_{+} |\Psi^{+}_{12 \cdots N} \rangle = { }^{\textstyle\ast}\langle z_{N+1}|
{ }^{\textstyle\ast}\langle z_{N+2}| \cdots { }^{\textstyle\ast}\langle z_n ||\Psi\rangle ,$$ is entangled for every choice of $|z_j\rangle^{\textstyle\ast}$ except for the case in which $\vartheta_j$ happens to be a multiple of $\pi$. In Eq. (25), $p_+$ is a normalization factor given by $$p_+ = c^2_1 \prod^{n}_{j=N+1} \cos^2 \left( \frac{\vartheta_j}{2} \right)
+ c^2_2 \prod^{n}_{j=N+1} \sin^2 \left( \frac{\vartheta_j}{2} \right) ,$$ while the state vector $|\Psi^{+}_{12 \cdots N} \rangle$ is found to be $$\begin{aligned}
|\Psi^{+}_{12 \cdots N} \rangle & = & p^{-1/2}_{+} \left[ c_1 \cos\frac{\vartheta_{N+1}}
{2} \cos\frac{\vartheta_{N+2}}{2} \cdots \cos\frac{\vartheta_{n}}{2} \right. \nonumber  \\
&& \times |z_1\rangle |z_2\rangle \cdots |z_N\rangle + c_2 (z_{N+1})(z_{N+2}) \cdots
(z_n)  \nonumber  \\
&& 