We've got 2 routes course/sections/trends and professor/sections/trends, which allowed for fast querying of sections from the aggregated collections trends_course_sections & trends_prof_sections.
Add another route professor-course/sections/trends which can query sections (with embedded course and professor objects) from collection trends_course_and_prof_sections , using the combination of professor and course's name.
You should also move all the trends-related routes under a single controller (and route) file for better management in the future.