= Solution
Use the total scattering angle $\psi=2\theta$. For a cubic <unit cell>, <Bragg's law> and the <Miller indices> give
$$
\sin^2\theta=\frac{\lambda^2}{4a_0^2}(h^2+k^2+l^2).
$$
The four measured values of $\sin^2\theta$, normalized to the first, are $1,1.330,2.655,3.649$. Multiplying by three gives approximately $3,4,8,11$, the initial allowed sequence for a <face-centered cubic lattice>:
$$
\{111\},\quad\{200\},\quad\{220\},\quad\{311\}.
$$
The FCC lattice factor is $1+(-1)^{h+k}+(-1)^{h+l}+(-1)^{k+l}$; it vanishes unless all three indices have the same parity. Thus the initial ratios differ from those of a primitive or body-centered cubic lattice. This is the conventional minimal cubic indexing; arbitrarily hiding additional weak reflections could make a short list alone ambiguous.
The low-pressure <rock salt structure> has an FCC <Bravais lattice> with one NaCl <formula unit> per <primitive unit cell>, or four per conventional cube. A possible <atomic basis of a crystal> is Na at zero and Cl at $(1/2,0,0)$ in conventional fractional coordinates. The two species have unequal <atomic scattering factors>, so both the odd and even FCC families can occur.
The four independent <lattice constant> estimates are
$$
a_0=\frac{\lambda\sqrt{h^2+k^2+l^2}}{2\sin(\psi/2)}
=(0.56312,\ 0.56386,\ 0.56436,\ 0.56446)\,\mathrm{nm}.
$$
Their small scatter reflects the rounded angular data. The appropriate reported result is
$$
\boxed{\text{FCC Bravais lattice},\qquad a_0\simeq0.564\,\mathrm{nm}.}
$$
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