Research your subject thoroughly before you begin your essay. Use information from multiple sources with opposing viewpoints. Include sources that directly advocate the radical thinking, as well as sources that oppose it. This will allow you to remain unbiased as you explore the subject. Also, research less extreme --- while related --- viewpoints. This will help you to explain and relate the radical thinking subject to your readers.
Explore the various aspects of radical thinking from the perspective of those who advocate it. Even if you wish to refute this viewpoint, it is important to present it to your readers from the genuine position of its advocates, so that your readers fully understand the implications of the viewpoint. Reference direct sources, so that your readers see the radical subject as being presented in an unexaggerated manner.
Explore various ways of thinking that are opposed to the radical viewpoint. Choose sources that directly reference and refute the ideas that advocate radical thinking. This presents your readers with both sides of the issue and helps them to better understand the extreme nature of the radical viewpoint you presented.
Explore your own thoughts on radical thinking if the essay prompt allows for it. Relate the various viewpoints discussed in your own words and elaborate further your own viewpoint in relation to the radical viewpoint you presented. Also, discuss some of the far-reaching implications of the radical viewpoint that were not directly presented in the earlier sections of your essay. This shows your readers a broader perspective stemming from the radical viewpoint, and also it shows that you fully understand the radical viewpoint and can therefore extrapolate from it.