Let K be a number field. The Grunwald problem for a finite group (scheme) G/K asks what is the closure of the image of H^1(K,G) → ∏_{v ∈ M_K} H^1(K_v,G). For a general G, there is a Brauer—Manin obstruction to the problem, and this is conjectured to be the only one. In 2017, Harpaz and Wittenberg introduced a technique that managed to give a positive answer (BMO is the only one) for supersolvable groups. I will present a new fibration theorem over quasi-trivial tori that, combined with the approach of Harpaz and Wittenberg, gives a positive answer for all solvable groups.