Find Clebsch-Gordan coefficients in Wigner-Eckart theorem

happyparticle
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

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