The space-air-ground integrated network (SAGIN) has gained widespread attention from academia and industry in recent years. It is widely applied in many practical fields such as global observation and mapping, intelligent transportation systems, and military missions. As an information carrier of air platforms, the deployment strategy of unmanned aerial vehicles (UAVs) is essential for communication systems' performance. In this paper, we discuss a UAV broadcast coverage strategy that can maximize energy efficiency (EE) under terrestrial users' requirements. Due to the non-convexity of this issue, conventional approaches often solve with heuristics algorithms or alternate optimization. To this end, we propose an iterative algorithm by optimizing trajectory and power allocation jointly. Firstly, we discrete the UAV trajectory into several stop points and propose a user grouping strategy based on the traveling salesman problem (TSP) to acquire the number of stop points and the optimization range. Then, we use the Dinkelbach method to dispose of the fractional form and transform the original problem into an iteratively solvable convex optimization problem by variable substitution and Taylor approximation. Numerical results validate our proposed solution and outperform the benchmark schemes in EE and mission completion time.