If $\alpha =\sin \left({\cot }^{-1}\left(\tan \left({\cos }^{-1}\frac{2}{3}\right)\right)\right)$  and $\beta =\sin \left(\cos e{c}^{-1}\left(\cot \left({\tan }^{-1}\frac{1}{3}\right)\right)\right)$  are the roots of the quadratic equation $a{x}^2+bx+c=0$  where a, b, c are integers and c is prime then the value of $(a + b + c)$equals