There are several ways to remove drastic brightness variations in a video, depending on the tools and software available to you. Here are some general steps that you can follow:

1. Use a video editing software: A video editing software, such as Adobe Premiere Pro, Final Cut Pro, or DaVinci Resolve, can help you to adjust the brightness and contrast of a video clip.

2. Apply color correction filters: Most video editing software comes with color correction filters that allow you to adjust the brightness, contrast, and color of a video clip. Use these filters to adjust the brightness of the video clip and reduce any drastic variations.

3. Use keyframing: Keyframing is a technique that allows you to adjust the brightness of a video clip over time. You can use this technique to gradually adjust the brightness of the video clip, reducing any drastic variations.

4. Use a plugin: Some video editing software comes with plugins that can help you to reduce drastic brightness variations in a video. For example, the Neat Video plugin can help you to reduce noise and grain in a video, which can help to reduce brightness variations.

5. Use manual adjustments: If you don't have access to a video editing software or plugins, you can still make manual adjustments to the brightness of a video clip using the brightness and contrast controls on your computer or TV. However, this method is less precise than using a video editing software or plugin.

Overall, the key to removing drastic brightness variations in a video is to adjust the brightness and contrast in a way that is consistent throughout the video clip. This may require some experimentation and tweaking, but with practice, you should be able to achieve a smoother and more even-looking video.