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.