Don’t use a calculator

$\cos{(30^{\circ})} = \sin{(60^{\circ})} = \dfrac{\sqrt{3}}{2}$ $\csc{(60^{\circ})} = \dfrac{1}{\sin{(60^{\circ})}} = \dfrac{1}{\frac{\sqrt{3}}{2}} = \dfrac{2}{\sqrt{3}} = \dfrac{2 \sqrt{3}}{3}$ $2+3-3 = \boxed{2}$

Since cos(30)=sin(60)= $\frac{\sqrt{3}}{2}$
and the value of $\csc \theta$ = $\frac{1}{\sin \theta}$ So csc(60)= $\frac{2}{\sqrt{3}}$ = $\frac{2\sqrt{3}}{3}$ ,
which gives a=2,b=3,c=3.