Surface Area of Parametric Equation

Calculus Level 3

\[\mathcal{P} := \begin{cases} y= \tan t \\ x = \sec t \end{cases}\]

The curve \( \mathcal{P} \) is defined using the above pair of parametric equations for all real values of \( t \) such that \( \cos t \neq 0\).

What is the surface area of the solid of revolution obtained by revolving \( \mathcal{P} \) about \( x\)-axis for \(0 < t < \frac{\pi}{4} \)?

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