On the coordinate plane, let $\Gamma$ be the graph of the cubic function $f(x) = x^{3} - 9x^{2} + 15x - 4$. Show that $P(1, 3)$ is a point on $\Gamma$, and find the equation of the tangent line $L$ to $\Gamma$ at point $P$.
On the coordinate plane, let $\Gamma$ be the graph of the cubic function $f(x) = x^{3} - 9x^{2} + 15x - 4$.\\
Show that $P(1, 3)$ is a point on $\Gamma$, and find the equation of the tangent line $L$ to $\Gamma$ at point $P$.