Let's first compute $\cos{C}$ by using the law of consine: \begin{align*} (a+b+c)(a+b-c) &= 3bc\\ (a+b)^2 - c^2 &=3bc\\ a^2 + b^2 + 2ab -c^2&= 3bc\\ a^2 + b^2 - c^2 &= bc\\ \frac{a^2 + b^2 - c^2}{bc} & = 1 \end{align*} Hence we know: $$\cos{C} = \frac{a^2 + b^2 - c^2}{2bc}=\frac{1}{2} \implies \boxed{C=\frac{\pi}{3}}$$