Hexapod robots have gained significant attention due to their potential applications in complex terrains and dynamic environments. However, traditional inverse kinematics approaches often face challenges in meeting the precision required for adaptive omnidirectional movement. This work introduces a novel approach to addressing these challenges through the Directed Angular Restitution (DAR) method. The DAR method offers significant innovation by simplifying the calculation of rotational transformations necessary for aligning vectors across different planes, thus enhancing control, stability, and accuracy in robotic applications. Unlike conventional methods, the DAR method extends the range of trigonometric functions and incorporates spin functions to ensure continuous and smooth trajectory tracking. This innovative approach has been rigorously tested on a hexapod robot model, demonstrating superior performance in movement precision and stability. The results confirm that the DAR method provides a robust and scalable solution for the inverse kinematics of hexapod robots, making it a critical advancement for applications in robotics and automation where precise control and adaptability are paramount.