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evaluate assuming odd integers?

Is there a way in Mathematica to evaluate an expression assuming some 
varialbe is Odd integer, for example in below integral how can i tell it 
that n is odd integer in the Assumptions section of FullSimplify command or 
the integral itself??:
Integrate[Sin[n*Pi*(z/L)], {z, 0, L}]
FullSimplify[%, n \[Element] Integers && n >= 0 &&
L \[Element] Reals && L > 0 && z \[Element] Reals]

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