Answer
$\theta =95.73^o$.
Work Step by Step
Let $u=(1,0,-3,0),\quad v=(2,-2,1,1), \quad \langle u, v\rangle=u\cdot v $.
The angle $\theta$ between $u$ and $v$ is given by the formula
$$\cos \theta=\frac{\langle u, v\rangle}{\|u\| \cdot\|v\|}=\frac{2+0-3+0}{\sqrt{ 1+0+9+0}\sqrt{ 4+4+1+1}}=\frac{-1}{\sqrt{ 100}}=\frac{-1}{10}.$$
That is, $\theta =95.73^o$.
