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Accurate closed-form approximations to the sum of independent identically distributed eta-mu and kappa-mu random variables are provided. The proposed approximations turn out to be simple, precise, and useful for obtaining important performance metrics of communications systems where sums of variates arise. In particular, average bit error rate and level crossing rate of multibranch equal-gain combining receivers are attained to illustrate the applicability of the approximations. Some sample examples show that the intricate exact solution and the simple approximate expressions yield results that are almost indistinguishable from each other.