I admit not to follow what you are doing.

So let's look at the actual definition of.radian

One radian is defined as the measure of the central angle inanycircle that subtends an arc of length equal to the radius of that circle.

Most of us in prefer that we all use radian measure and not use degrees.

That is not a popular position in themathematics educationcommunity.

But among professional mathematicians it is the universal option.