2000017209

For what real value of $a$ is the following matrix an upper triangular matrix? $$\left(\begin{array}{ccc}{2}^{a-3}& 3+a& a-2\\ 3-a& (\sqrt{3}{)}^{a-1}& 1+a\\ \sin (\pi a)& a-\sqrt{9}& 2+\sqrt{3}\end{array}\right)$$