The integrated optical gyroscope is a highly possible way to achieve chip-level gyroscopes. We proposed and simulated a three-dimensional Si3N4 optical interconnect platform. It transforms the waveguide coil from a single-layer structure to a multi-layer structure, which can increase the sensing area of the coil under the same footprint. The proposed platform with low interlayer transition loss and crossing loss can reduce the overall loss in the coil and improve the theoretical angular random walk (ARW). A quadruple-layer sensing coil with a maximum radius of 30 mm and a total length of 2.08 m is derived, which can attain an ARW of 0.15 deg/√h and an insertion loss of 3.15 dB in theory.