The major product formed in the following reaction is

Mechanism:

→Step 1: Attack of lone pair of oxygen to BF₃ .OEt.

→Step 2: Epoxide opening: It can ocur in two ways 'a' and 'b'.

'a' will lead to the formation of less steble tertiary carbocation, hence, the corresponding product is unfavourable.

'b' path will lead to the formation of more stable tertiary carbocation, hence, will lead to the formation of favourable product.

→ 'a' leads to formation of unfavourable product.

→ 'b' leads to the formation of favourable product.

→ After methyl shift Carbocation generation can also occur on bridgehead carbon which but that is also highly unstable, thus forms unfavourable product.

Conclusion:
The correct answer is option 1.