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I'm thinking out loud here and haven't solved this yet.  This answer is logging my process as I try to solve the problem.  It may very well result in the same long-winded process you went thru.  Nothing shrewd or insightful is promised.

There are three unknowns (R1, R2, R3), and there are fortunately three constraints:<ol>

<li>The impedance looking into the input must be Rin:

 &nbsp; &nbsp; R1 + R3//(R2 + RL) = Rin

<li>The impedance looking into the output must be RL:

 &nbsp; &nbsp; R2 + R3//(R1 + Rin) = RL

<li>The attenuation must be A.  I think it will be nicer to use gain rather than attenuation, so I'll use G = 1/A.  This constraint is more tricky to write down in a single equation, so I'll use two and the intermediate value Gx.  Gx is the gain from the input to the mid point:

 &nbsp; &nbsp; Gx = R3//(R2 + RL) / [Rin + R1 + R3//(R2 + RL)]

Then the gain at the output is:

 &nbsp; &nbsp; G = Gx * RL / (R2 + RL)

</ol>

Yeah, that looks like it's going to be messy.

The first step is to combine the two equations of constraint three into one, which gets rid of the intermediate value Gx I used for convenience.  Actually that part is easy since its just a straight multiply.  Like I said, this is thought stream dump.  Breaking the third constraint into two wasn't necessary, although it does document the separate thoughts.  Anyway, simplified constraint 3 is:

--- Work in progress ---<br>
I'll get back to this.  I also need to look up how to use MathJax, since these equations are getting too complicated for plain HTML.