If you ignore the renewable option, and just treat it as a 3-month long policy which starts on 1/12, then (assuming risk uniform) the UPR at 31/12 would be 2/3 of the premium paid.
Adding the 'renewable option' bit is very unusual (for general insurance). But anyway, how the policy would be treated would depend on the purpose of the valuation and the accounting principles guiding them. These are called 'boundary conditions' - where/when a policy is deemed to 'start' and 'finish', and the rules could vary (eg IFRS4, IFRS17 or Solvency II). This is covered further in Subject SA3. You might also want to see the Subject SA3 exam paper in September 2017 (Q1), where this was explicitly examined (in the context of Solvency II).