A simple problem for a simple day

Geometry Level 4

Angles \( \alpha = a°, \beta = b° \) and \( \gamma = c° \) belong to a triangle and satisfy the following:

  1. \( \sin{\alpha} \times \sin{\beta} \times \sin{\gamma} = \frac{3 - \sqrt{3}}{8} \)

  2. \( \sin{2\alpha} + \sin{2\beta} = \frac{3}{2} \)

Sumit your solution in form: \( c + R(a, 17) + R(b, 17) \).

Function \( R(x, y) \) has a value of remainder when \( x \) is divided by \( y \).

e. g. \( R(13, 4) = 1 \), \( R(45, 5) = 0 \)

Inspiration: Solution section.

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