Calculate \(\mathbf{T}_{u}, \mathbf{T}_{v}\), and \(\mathbf{N}(u, v)\) for the parametrized surface at the given point. Then find the equation of the tangent plane to the surface at that point.

\(\Phi(r, \theta)=\left(r \cos \theta, r \sin \theta, 1-r^{2}ight) ; \quad r=\frac{1}{2}, \quad \theta=\frac{\pi}{4}\)