You gave two written talaqs to your wife; accordingly, two revocable talaqs (talaq-e-raj’i) took place. After the talaq if the iddah period is over, the woman became bayinah (separated) and your nikah came to an end completely. The third talaq shall be invalid. In case the iddah is not over, then too there is no need for the third talaq, since she will ultimately become bayinah when the iddah is over, but if you give it within the iddah it shall take place.
Allah (Subhana Wa Ta’ala) knows Best
Darul Uloom Deoband