Unsympathetic Trigonometric Arithmetic

Geometry Level 4

\[ \large 2\cot^{-1} \left( \frac{\displaystyle \sum_{j=1}^{44} \cos(j^\circ) }{\displaystyle \sum_{k=1}^{44} \sin(k^\circ) } \right) = x^\circ \qquad , \qquad x = \ ? \]

All angles are measured in degrees.

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