Cloth manipulation is a challenging task due to the deformable and high-dimensional nature of cloth, which leads to complex interaction dynamics and perceptual ambiguity arising from frequent occlusions of critical visual cues such as folds, edges, and grasp points. In this work, we tackle cloth unfolding using a regrasping-in-the-air strategy, where one manipulator holds the cloth while the other grasps it at an optimally selected point to unfold it. To this end, we propose CeDiRNet-6DoF, a deep learning framework that jointly predicts effective grasp points and the complete 6-DoF grasp pose from the observed cloth configuration. By integrating dense 3D grasp regression with segmentation and sine-cosine-encoded Euler angles, the proposed method reliably estimates the grasp configuration that maximizes the unfolded cloth area. We extensively evaluated CeDiRNet-6DoF on a bimanual robotic setup within the ICRA 2024 Cloth Competition framework, achieving state-of-the-art performance. An ablation study further validates the benefits of key design components, including joint segmentation, background randomization, and image cropping. These results establish CeDiRNet-6DoF as a robust and versatile foundation for reliable robotic cloth manipulation in unstructured environments.

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