1. The problem is to evaluate the integral $$I = \int \tan(\tan t) \cdot t \, dt$$. 2. This integral involves a composition of trigonometric functions and a polynomial term, which is not a standard integral and does not have a straightforward elementary antiderivative. 3. The function $$\tan(\tan t)$$ is highly non-linear and does not simplify easily. 4. Common techniques such as substitution, integration by parts, or series expansion do not yield a closed-form solution in elementary functions. 5. Therefore, this integral cannot be expressed in terms of elementary functions and is considered non-elementary. 6. To evaluate it for specific limits, numerical methods or approximation techniques would be necessary. 7. In summary, the integral $$\int \tan(\tan t) \cdot t \, dt$$ does not have a closed-form solution in elementary functions.