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Consider on the first quadrant of the trigonometric circle the arcs AM_1 = x_1,AM_2 = x_2,AM_3 = x_3, \ldots , AM_v = x_v , such that x_1 < x_2 < x_3 < \cdots < x_v. Prove that
\sum_{i=0}^{v-1} \sin 2x_i - \sum_{i=0}^{v-1} \sin (x_i- x_{i+1}) < \frac{\pi}{2} + \sum_{i=0}^{v-1} \sin (x_i + x_{i+1})

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