Is my calculated capacitor sign correct?
The method you've used looks tedious.

Do you know the value of R? If so, you can determine the total current by Ohm's law.

$$I=\frac{V_{ina}-V_{inb}}{R}$$ 

So, now you know the voltage across the parallel circuit (\$\small V_{inb}\$) and the total current through it, so you can calculate its impedance by Ohm's law.

You can also find find the impedance of the parallel circuit by simple circuit analysis. 

Finally, equate the two (complex) impedance expressions to find the values of Cs and Rs.