Logarithm + Trigonometry = Summation

Geometry Level 4

\[\begin{eqnarray} \large &&\log_{2}{(1+\cot{46^{\circ}})} \\ \large&+&\log_{2}{(1+\cot{47^{\circ}})}\\ \large &+&\log_{2}{(1+\cot{48^{\circ}})} \\ \large &+&\ldots \\ \large &+&\log_{2}{(1+\cot{89^{\circ}})}\\ \large &=&\ ? \end{eqnarray}\]

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