Geometry or calculus?

Calculus Level 3

\[\large \int_{{0}^{\circ}}^{{53}^{\circ}} \left(\dfrac{\tan x}{1 - \cot x} + \dfrac{\cot x}{1 - \tan x} - 1\right)\dfrac{{\sin}^2 x}{\cos x} \, dx\]

Evaluate the definite integral above to two decimal places.

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