Series involving Zeta and Eta of Odd Numbers

<i>In this paper, three expressions from Euler for the sine or cosine function are used as a starting point for a search towards an expression for </i><i>𝜁</i><i>(3) : the identity function, the product formula and the reflection formula. More specific : does there exist an expression for</i><i> 𝜁</i><i>(3) only in terms of constants, such as a rational, </i><i>π</i><i>, </i><i>𝛾</i><i>, e, ln(2), perhaps even i , … without summations or integrals ?</i><i> </i><i>Starting from Euler’s Reflection formula, this paper explains how to obtain an equation for a sum involving only Zeta of odd natural numbers. Also an equation involving Eta of odd natural numbers is obtained by applying the logic of a proof for ZE1(1)-ZE1(2).</i>