Question: solve trigonometric system of equation with conditions

I want to solve this equation with assumptions!!!

restart;
assume(d::real, d>0):
assume(a::real, -0.01 < a, a < 0):
sys:={-800*Pi*a*cos(6.557377048*Pi*(3.470797713+d))/(a+1)^3 = -.9396060697, 800*Pi*a*sin(6.557377048*Pi*(3.470797713+d))/(a+1)^3 = -.3238482794};
solve(sys, {a,d},useassumptions=true, AllSolutions=true);

one of the solutions has true "a" but "d" is wrong, I want one true solution!

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