$\sin{\alpha}+\sin{\beta}+\sin{\gamma}>2$ Where $\alpha$, $\beta$ and $\gamma$ are angles from an acute-angled triangle.

$\sin\left(\alpha\right) \geq 2\alpha/\pi\,,\quad\sin\left(\beta\right) \geq 2\beta/\pi\,,\quad\sin\left(\gamma\right) \geq 2\gamma/\pi$.

$$ \sin\left(\alpha\right) + \sin\left(\beta\right) + \sin\left(\gamma\right) \geq 2\,{\alpha + \beta + \gamma \over \pi} = 2 $$

The equal $\left(~=~\right)$ sign is excluded since it requires $\alpha = \beta = \gamma = 0$ or $\alpha = \beta = \gamma = \pi/2$ which do not satisfy the problem conditions.

Then $$ \begin{array}{|c|}\hline\\ \color{#ff0000}{\large\quad% \sin\left(\alpha\right) + \sin\left(\beta\right) + \sin\left(\gamma\right) \color{#000000}{\ >\ } 2\quad} \\ \\ \hline \end{array} $$