Question about how to construct global angular form

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In Bott&Tu 's book "Differential form in Algebraic Topology", he used the Global angular form to compute the euler class and euler characteristic. I understand how to deduce the euler class after constructing the global angular form for the sphere bundle, but I have trouble with constructing the form explicitly. Can anyone provide some examples of global forms to help me understand? For example, CP^1 or something else?