To find the intersection points of the curves \(y = \tan^2(x)\) and \(y = 4 - x^2\), we need to solve the equation:
\[ \tan^2(x) = 4 - x^2 \]
Let's denote \(f(x) = \tan^2(x)\) and \(g(x) = 4 - x^2\). Then, we need to find the values of \(x\) such that \(f(x) = g(x)\).
Since solving this equation analytically may be challenging, we can use numerical methods or graphing tools to approximate the intersection points.
Let's plot the two curves and find their intersection points:
