You are a little out of whack here. I think you are trying to define the lower case Greek letter as meaning radians. Not so. is nothing more than a dimensionless transcendental irrational number representing the ratio of a the circumference of a circle to its diameter. I think you are making the association because angle measures expressed in radians frequently are expressed as some multiple of . This is because a complete circle is measured as radians.
Having said all of that, I think you are asking to find the exact value of the expression:
So, instead of going 7/8 of the way around the circle clockwise, go 1/8 of the way around counter-clockwise and get to the same place, namely .
Then from the unit circle we can see that:
and
And since we know that
We can see that
John
My calculator said it, I believe it, that settles it