M000003520
$$\pi=12\arctan\left(\frac{1}{5}\right)+8\arctan\left(\frac{1}{15}\right)-4\arctan\left(\frac{1}{18}\right)+12\arctan\left(\frac{1}{21}\right)-4\arctan\left(\frac{1}{34}\right)-4\arctan\left(\frac{1}{55}\right)+8\arctan\left(\frac{1}{81}\right)-8\arctan\left(\frac{1}{467}\right)$$