A circle of radius $R=4$ is centered at the origin. An equilateral triangle is inscribed in this circle. A rectangle with dimensions $3\times 5$ is placed such that its bottom-left corner is at $(-2,-2)$. The shaded area is the area of the circle, minus the area of the equilateral triangle, plus the area of the rectangle. This area can be expressed in the form $\frac{a}{b}\cdot \pi -\sqrt{c}+d$, where $a$, $b$, $c$, and $d$ are positive integers and $a$ and $b$ are relatively prime. What is $a+b+c+d$?