A Manhattan world lying along cuboid buildings is useful for camera angle estimation. However, accurate and robust angle estimation from fisheye images in the Manhattan world has remained an open challenge because general scene images tend to lack constraints such as lines, arcs, and vanishing points. To achieve higher accuracy and robustness, we propose a learning-based calibration method that uses heatmap regression, which is similar to pose estimation using keypoints, to detect the directions of labeled image coordinates. Simultaneously, our two estimators recover the rotation and remove fisheye distortion by remapping from a general scene image. Without considering vanishing-point constraints, we find that additional points for learning-based methods can be defined. To compensate for the lack of vanishing points in images, we introduce auxiliary diagonal points that have the optimal 3D arrangement of spatial uniformity. Extensive experiments demonstrated that our method outperforms conventional methods on large-scale datasets and with off-the-shelf cameras.