Find viewing direction that sees most points

You are standing at the origin on a 2D plane. You are given a list of points `points[i] = (xi, yi)` (not necessarily distinct), and a viewing angle `theta` in degrees. You may choose any viewing **direction** (a ray starting from the origin). Your field of view is the **closed sector** of angular width `theta` whose central axis is your chosen direction (equivalently, a window of size `theta` when sweeping directions around the origin). A point is considered **visible** if the angle from the positive x-axis to the vector `(xi, yi)` lies within that angular sector (after choosing the sector’s placement). Points exactly on the boundary are visible. If any points are exactly at the origin `(0,0)`, they are always visible regardless of direction. **Task**: Choose a viewing direction that maximizes the number of visible points. **Output**: - Return the maximum number of visible points, and - Return any one viewing direction (e.g., an angle in degrees in `[0, 360)`) that achieves this maximum. **Constraints (typical interview scale)**: - `1 <= n <= 2e5` - `xi, yi` are integers (e.g., in `[-1e9, 1e9]`) - `0 < theta <= 360` Notes: - Angles wrap around at `360°`. - Your solution should be better than `O(n^2)`.