Trigonometric Summation

Geometry Level 4

The following sum

\[ \sum_{n = 1}^{\infty} \frac {\cos (n \theta)} { 2^n} \]

can be expressed as

\[ \frac{A \cos(\theta) - B} {C - D \cos(\theta)} \]

where A, B, C, and D are positive integers, and are the smallest possible. Find A + B + C + D.

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