effective number of relativistic degrees of freedom is equal to $3.046$.

Using this reference model we find the values $\theta_{E}^0=1.518^\circ$ for $\delta z = 0$ and $\theta_{E}^{\delta z}=1.504^\circ$ for $\delta z = 0.05$. The shift obtained is $0.014^\circ$, i.e., the projection effect is almost negligible since it produces a shift in the BAO angular position of $\Delta \theta(\overline{z}, \delta z)\,=\,0.9\%$.

Cosmological constraints {#CC}
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Here we measured a new angular acoustic scale, $\theta_{\mbox{\footnotesize\sc bao}}$ at $\overline{z} = 2.225$. We combine this new measurement with other eight data points provided by [@Carvalho; @Alcaniz] (obtained following the same quasi-independent model approach) to constrain parameters in the cosmological models with constant and variable equations of state, namely wCDM and w$(a)$CDM models.

For the w$(a)$CDM model we assume the Barboza-Alcaniz parametrized equation of state [@BarbozaAlcaniz]: ${\rm w}(a) = {\rm w}_0 + {\rm w}_a [(1- a) / (2a^2 - 2a + 1)]$. The relation between the angular BAO scale, $\theta_{\mbox{\footnotesize\sc bao}}$, and the angular diameter distance, $D_A$, is obtained using the expression $$\theta_{\rm BAO}(z) = \frac{r_s(z_{drag})}{(1+z) \, D_A(z)} \, ,$$ where $r_s(z_{drag})$ is the comoving sound horizon at the end of baryon drag, and is provided by CMB measurements. To constrain the cosmological parameters we 