M000003580
$$\pi=4\arctan\left(\frac{1}{2}\right)+8\arctan\left(\frac{1}{3}\right)-4\arctan\left(\frac{1}{5}\right)+4\arctan\left(\frac{1}{18}\right)-4\arctan\left(\frac{1}{21}\right)-8\arctan\left(\frac{1}{23}\right)-4\arctan\left(\frac{1}{47}\right)-8\arctan\left(\frac{1}{83}\right)$$