6. [1/2 Points]
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PREVIOUS ANSWERS SCALC9 4.5.034.
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Evaluate the indefinite integral. (Use $C$ for the constant of integration.)
\[
\int \tan ^{2}(\theta) \sec ^{2}(\theta) d \theta
\]

Step 1 ：The integral involves the functions \(\tan^2(\theta)\) and \(\sec^2(\theta)\). We know that \(\sec^2(\theta)\) is the derivative of \(\tan(\theta)\). This suggests that we can use a substitution method to solve the integral. We can let \(u = \tan(\theta)\), then \(du = \sec^2(\theta) d\theta\). The integral then becomes \(\int u^2 du\), which is a simple power rule integral.

Step 2 ：The integral of \(u^2\) with respect to \(u\) is \(\frac{u^3}{3}\). However, we need to substitute \(u\) back with \(\tan(\theta)\) to get the integral in terms of \(\theta\).

Step 3 ：The integral of \(\tan^2(\theta) \sec^2(\theta)\) with respect to \(\theta\) is \(\frac{\tan^3(\theta)}{3}\). However, we need to add the constant of integration \(C\) to the result.

Step 4 ：The indefinite integral of \(\tan^2(\theta) \sec^2(\theta)\) with respect to \(\theta\) is \(\boxed{\frac{\tan^3(\theta)}{3} + C}\).