The two-photon transition $psi(3686)togammagamma J/psi$ is studied in a sample of 106 million $psi(3686)$ decays collected by the BESIII detector. The branching fraction is measured to be $(3.1pm0.6(unit{stat})^{+0.8}_{-1.0}(unit{syst})) times10^{-4}$ using $J/psito e^+e^-$ and $J/psitomu^+mu^-$ decays, and its upper limit is estimated to be $4.5times10^{-4}$ at the 90% conference level. This work represents the first measurement of a two-photon transition among charmonium states. The orientation of the $psi(3686)$ decay plane and the $J/psi$ polarization in this decay are also studied. In addition, the product branching fractions of sequential $E1$ transitions $psi(3686)togammachi_{cJ}, chi_{cJ}togamma J/psi (J=0,1,2)$ are reported.
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