AT-OEMO-FED1 2007 Problem 4

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