Not sure if this can help you but basic trigonometry jammed with complex numbers helped me do this during my high school (some topic called nth roots of unity). That gives an intuitive understanding of trapping regular polygons inside the unit circle.
@resboy2445 This is exactly what I wanted to say, but in a broader sense you can use the Argand plane to understand it. @TfGuy44 explained the angles in a very comprehensive way, but for deeper understanding, you may refer to roots of unity.
@TfGuy44 Was browsing generally and came across this wonderful method of understanding trig. Beautifully explained!! Thank you for taking the time to explain in such detail. Enjoyed reading. Also hungry now and ordered a pizza! There goes the circumference of my waistline
