Trigonometric Complex

Algebra Level 3

\[\begin{cases} \color{green}a = \cos\theta + \iota\sin\theta \\ \color{blue}b = \cos\phi + \iota\sin\phi \\ \color{magenta}c = \cos\Psi + \iota\sin\Psi \\ \dfrac{\color{green}a}{\color{blue}b} + \dfrac{\color{blue}b}{\color{magenta}c} + \dfrac{\color{magenta}c}{\color{green}a} = 2 \end{cases}\]

\[\large \sin(\theta - \phi) + \sin(\phi - \Psi) + \sin(\Psi - \theta) = ? \]

Details:

  • \(\iota = \sqrt{-1}\).
  • Put the answer upto 2 decimal places.
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