Let n>4 be a non-negative integer. Given is the in a circle inscribed convex n-gon A_0A_1A_2\dots A_{n \minus{} 1}A_n (A_n \equal{} A_0) where the side A_{i \minus{} 1}A_i \equal{} i (for 1≤i≤n). Moreover, let ϕi be the angle between the line A_iA_{i \plus{} 1} and the tangent to the circle in the point Ai (where the angle ϕi is less than or equal 90o, i.e. ϕi is always the smaller angle of the two angles between the two lines). Determine the sum
\Phi \equal{} \sum_{i \equal{} 0}^{n \minus{} 1} \phi_i
of these n angles. geometry unsolvedgeometry