An all-optical method is proposed for destabilizing the period-one (P1) nonlinear dynamic state using a system of three cascaded semiconductor lasers across two optical injection stages.Leveraging the P1 dynamic state in the first optical injection stage as a tunable microwave oscillator, this approach generates broadband chaotic dynamics without the need for high-frequency microwave sources.By tuning the second injection stage such that the lower oscillation sideband of the injecting P1 state is Soft Drinks offset by a few gigahertz from the injection-shifted cavity resonance of the second laser operating also in the P1 dynamic state, the P1 state is destabilized into a chaotic dynamic state.The resulting dynamics are influenced by both the power and frequency of the lower oscillation sideband of the injecting P1 state, leading to a Waxed Hats cascade of period-doubling bifurcations that culminate into chaos.The induced chaos exhibits broad standard and effective bandwidths exceeding 30 GHz and 15 GHz, respectively, highlighting the potential of this approach for applications in broadband chaotic systems.