You may have incorrectly simplified the calculation, or you may have confused the values of sine at $\displaystyle{{30}}^{\circ}\usepackage{cmbright}\Huge\$ and $\displaystyle{{60}}^{\circ}\usepackage{cmbright}\Huge\$ . Rewrite $\displaystyle{\sin{{\left(\frac{{{11}\pi}}{{3}}\right)}}}\usepackage{cmbright}\Huge\$ as $\displaystyle{\sin{{\left({2}\pi+\frac{{{5}\pi}}{{3}}\right)}}}\usepackage{cmbright}\Huge\$ and then use the identity $\displaystyle{\sin{{\left(\theta+{2}\pi\right)}}}={\sin{\theta}}\usepackage{cmbright}\Huge\$ to simplify the calculation.