Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 146 / 1 / e / Solution

Take the toruswith the translation-invariant symplectic formThe coordinate vector fields give a global symplectic frame of $TM$, so $TM$ is symplectically trivial. Passing fiberwise to the Lagrangian Grassmannian bundle giveswhich is a smooth trivialization over the compact symplectic manifold $T^{2n}$.