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Actually, you do not need any other equation. The non-trivial solution is possible with three equations since you would want the gain in terms of the ratio of Vout and Vin. Also, you should notice that you have accounted for all the nodes in the circuit. There are no other nodes for you to write an equation on. Nor, there is any other relationship which will help you.
By the way, are you trying to solve Nested Miller compensation techniques
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