= Solution
A ring-retaining bromination replaces the three hydridic B–H positions while preserving N–H. Its net stoichiometry is
$$
\boxed{\mathrm{B_3H_3N_3H_3}+3\mathrm{Br_2}\longrightarrow\mathrm{B_3Br_3N_3H_3}+3\mathrm{HBr}.}
$$
Use controlled bromination and conditions allowing elimination of hydrogen bromide from addition intermediates, rather than identifying the first <bromine> adduct as the final ring product. Boron-bound hydrogen has <hydride>-like character because boron is less electronegative than hydrogen; its replacement is consistent with electrophilic attack by <bromine>. The primary preparative work reports B-tribromoborazines obtained by bromination of <borazine> and its N-methyl analogue.<B-Tribromoborazines from the Bromination of Borazine and N-Trimethylborazine by Reed F. Riley and Carl J. Schack>[1964, pp. 1651–1653, bromination and formation of B-tribromoborazines]{ref}
\b[The product must retain the unsaturated B$_3$N$_3$ ring.] Merely adding three HBr molecules to <borazine> initially gives a saturated hydrogen-halide addition product, not the required formula. Addition followed by suitable elimination is distinct from simply asserting direct B–H protonolysis by HBr.
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