Find Clebsch-Gordan coefficients in Wigner-Eckart theorem

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Homework Statement:

Find Clebsch-Gordan coefficients $\langle j,1;m,0| j',m' \rangle$

Relevant Equations:

$\langle j,1;m,0| j',m' \rangle$

Hi,
I spent the entire day trying to figure out how to find the Clebsch-Gordan coefficients.

For example, if I have something like $\langle 1,1;2,0|2,1 \rangle$ I know how to find it in a table.
However, here I have $\langle j,1;m,0| j',m' \rangle$

I found that $\langle j,1;m,0| j',m' \rangle = \frac{m}{\sqrt{j(j+1)}}$, but I have no idea how they get it. They just throw this answer without explanation.


Edit: while looking for explanation on the internet I found the same homework that I'm trying to do, but this time there is a in-between problem with this hint : $|j,j \rangle = ( \sqrt{j} |j,1;j,0 \rangle - | j,1; j-1,1 \rangle)$

So I'm guessing that with this hint and $\langle j,1;m,0| j',m' \rangle$ I could find what I'm looking for, but I'm not sure how and I don't even know how to get $|j,j \rangle = ( \sqrt{j} |j,1;j,0 \rangle - | j,1; j-1,1 \rangle)$

Thank you