Is there a "radial projection" feature in sketch?

I have a sketch that has cyclic symmetry and would like to project the sketch onto a plane that is rotated at some small angle. However when using the regular "projection" feature, the sketch is projected orthogonally with respect to its original plane; I don't want that. I want it projected so that the cyclic symmetry is maintained.

 

I've included a drawing of what I'd like to perform; on the left is the usual orthogonal projection, and on the right is the radial projection. 

As part of the migration from the legacy Forum to the new SOLIDWORKS Forum, there was an overlap in timing where the new Forum was being loaded with historical data from an export migration, while at the same time, the legacy Forum was still operating during the period of March 12th to March 31st. Due to the overlapping timelines and import-export technical issues, posts during that time-frame could not have their media imported. If you created a post in the legacy Forum during that time-frame and wish to update the post in the new Forum with supporting media, please go to your post in the new Forum, enter into Edit mode and re-add any supporting media you want to insert.

The easiest way to find your posted content is: from the new Forum, click on your profile icon in the top right of the GUI, then select "My Profile" and you will be taken to the "Overview" tab where you can see all of your posting history.

Thank you