Determine the maximum angle θ for which the light rays

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Determine the maximum angle ϴ for which the light rays incident on the end of the light pipe in the figure are subject to total internal reflection along the walls of the pipe. Assume the light pipe has an index of refraction of 1.36 and the outside medium is air.
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I do not understand how the light is able to enter the tube. If the critical angle for a transition from the material of the tube is 47.33. why would all the light not be reflected back off of the pipe if the incident angle was 67°?

coleharlow
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working out the final solution using the inverse of sin does not work on a calculator, im from the UK.

darcey