On the equivalence between $Theta_{n}$-spaces and iterated Segal spaces

We give a new proof of the equivalence between two of the main models for $(infty,n)$-categories, namely the $n$-fold Segal spaces of Barwick and the $Theta_{n}$-spaces of Rezk, by proving that these are algebras for the same monad on the $infty$-category of $n$-globular spaces. The proof works for a broad class of $infty$-categories that includes all $infty$-topoi.