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In this paper we consider the orthogonal cooperative broadcast channel with a common message. The downlink and cooperation channels are modelled by erasure channels and assumed to be orthogonal. We derive an achievable rate for this channel by using a combination of decode-and-forward and estimate-and-forward and considering both symmetric and asymmetric cooperation. These schemes are based on a two-step cooperation. It is shown under which conditions the proposed achievable rate coincides with the considered upper bound that is in fact the interpretation of the traditional cut-set bound in the context of broadcast cooperative erasure channels. Moreover we propose a time-sharing-based iterative coding scheme with more than two cooperation steps.