Question 2
A convex heptagon is given. One calculates the cosines of four arbitrary its angles, the sines of three remaining angles, and then finds the sum of these 7 numbers. It happens that this sum is independent of the choice of the four angles. Prove that this heptagon has four equal angles.
Schematic convex heptagon (the sum condition is specified in the text):
Schematic convex heptagon (the sum condition is specified in the text):