You need to provide appropriate content-type for every PUT and POST requests
To modify ExtNet use fiollowing content-type:
Content-Type: application/vnd.vmware.admin.vmwexternalnet+xml
To Update Extnet,
1. Get all Extnets
https://x.x.x.x/api/admin/extension/externalNetworkReferences
2. Select the extNet you want to update
PUT https://x.x.x.x/api/admin/extension/externalnet/<<uuid of extnet>>
Content-type:application/vnd.vmware.admin.vmwexternalnet+xml; charset=UTF-8