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We prove results concerning entire solutions of non-linear binomial differential equations that have connections to trigonometric identities. We also prove a double inequality for the growth of entire solutions of non-linear monomial differential equations. Some open questions are posed.

In this paper, we deal with the problem of uniqueness of meromorphic functions sharing three values, and prove some results which are improvements and extensions of many known theorems. Examples are provided to show that the results in this paper are sharp.