Definitely tougher than previous one

Geometry Level 5

\[ \sum_{n = 1}^{K} \frac {\sin (n \theta)} { 2^n}\,=\,\dfrac{a^{K+1}\cdot \sin(\theta)\,+\,\sin(K \theta)\,-\,a \cdot \sin((K+1)\theta)}{2^{K}(b-c \cdot \cos(\theta))} \]

The equation above holds true for constants \(a,b,c\) and \(\theta\). Find the value of \(a+b+c\).


Inspiration.

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