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Hi ,Here I used A instead of theta.
2sec²A - sec⁴ A - 2cosec²A + cosec⁴A
=2(1+tan² A)-(1+tan²A)²-2(1+cot²A)+(1+cot²A)²
=2+2tan²A-1-tan⁴A-2tan²A-2-2cot²A+1+
cot⁴ A+2cot²A
after simplification ,
= cot⁴ A - tan⁴A
option ( 4 ) is correct
I hope this helps you.
: )