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No, you may not do this.
You are limited to a maximum of 90 days within the 180 day period regardless of how many trips those days occur over.
This is very clearly stated out on the Turkish Ministry of Foreign Affairs website :
- The length of stay provided by visa or visa exemption cannot exceed 90 days within each 180 days. The regulation of 90 days of stay within the last 180 days is binding for all foreigners that will travel to Turkey.
In order to stay longer you will need to apply for a "Short Term Residence Permit" which the link above contains some information about.