The first observation of the $B^0_stoetaeta$ decay is reported. The study is based on a sample of proton-proton collisions corresponding to $3.0$ ${rm fb^{-1}}$ of integrated luminosity collected with the LHCb detector. The significance of the signal is $6.4$ standard deviations. The branching fraction is measured to be $[3.31 pm 0.64,{rm (stat)} pm 0.28,{rm (syst)} pm 0.12,{rm (norm)}]times10^{-5}$, where the third uncertainty comes from the $B^{pm}toeta K^{pm}$ branching fraction that is used as a normalisation. In addition, the charge asymmetries of $B^{pm}toeta K^{pm}$ and $B^{pm}tophi K^{pm}$, which are control channels, are measured to be $(-0.2 pm1.3)%$ and $(+1.7pm1.3)%$, respectively. All results are consistent with theoretical expectations.
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