# Constant Shenanigans!

Geometry Level 4

$\large \sum_{k=1}^{1000} \sqrt{\sqrt[\phi]{(k^{1 + \sqrt{5}})}\left(\dfrac{\left[(1+\sin(k\tau))(1-\sin(k\tau)\right]^{\left \lfloor \pi \right \rfloor}}{\left[\frac{1}{2}(e^{ik\tau} + e^{-ik\tau})\right]^{2\left \lfloor e \right \rfloor}}\right)} = \ ?$

Details and Assumptions:

• $\tau$ is the almighty circle constant.

• $\pi$ is the lesser circle constant.

• $\phi$ is the golden ratio.

• $e$ is the base of the natural logarithm.

• $i$ is the imaginary unit.

• $\lfloor x \rfloor$ is the greatest integer function.

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