Answer
$\theta =\pi+2n\pi=(2n+1)\pi$, $n$ is an integer.
Work Step by Step
Let $u=(10,-5,15),\quad v=(-2,1,-3), \quad \langle u, v\rangle=u\cdot v $.
The angle $\theta$ between $u$ and $v$ is given by the formula
$$\cos \theta=\frac{\langle u, v\rangle}{\|u\| \cdot\|v\|}=\frac{-20-5-45}{\sqrt{ 100+25+225}\sqrt{ 4+1+9}}=\frac{-70}{\sqrt{ 4900}}=-1.$$
That is, $\theta =\pi+2n\pi=(2n+1)\pi$, $n$ is an integer.