Complex numbers ,how to find argument

Question

Given that $z = \dfrac{8+3i}{4-9i}$ Find the value of arg$(z^{2})$

I got $6.16$, answer is half of it

My working

Arg$(z)= 0.358 + 2.72 = 3.08$

So arg$(z^{2}) = 3.08(2)$.

Answer 1

$\arg z=\arg(8+3i)-\arg(4-9i)\approx0.35877+1.15257=1.51134$

so $\arg z^2\approx3.02268$