Mobile network operators today need to deliver new types of multimedia content, such as 360° video, to an ever-growing population of users. This creates a pressing need for network mechanisms that can support such demanding services in an economically-efficient fashion. This work focuses on applications that deliver a video file concurrently to multiple users which can utilize different radio technologies, namely cellular and Wi-Fi networks. We propose a mechanism for the orchestration of LTE multicast and Wi-Fi unicast transmissions by optimizing jointly: the design of multicast groups, the spectrum and bandwidth management in both networks, and the video encoding quality for each user (or, group). We consider two key performance criteria: minimizing the utilized LTE spectrum resources, and maximizing the delivered video quality. We formulate the respective optimization problems, prove they are NP-hard, and design an exact algorithm for solving them in near-real time. We employ a wealth of simulation experiments, using 3GPP-compliant parameters, that compare our approach with state-of-the-art benchmarks. Our findings suggest that, in representative scenarios, this multi-RAT orchestration can save up 55% LTE radio resources and increase up to 46% the delivered video quality.