Solve the equation 3 sec² (2θ + π/6) = 4 for -π/2 < θ < π/2, giving your answers in terms of π.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

1. [5] B1 cos(2θ+π/6) = (±)√3/2 oe
2. [5] B1 tan(2θ+π/6) = (±)1/√3 oe
3. [5] M1 for a correct order of operations, may be implied by one correct solution.
4. [5] A1 for 1 correct solution.
5. [5] A1 for a 2nd correct solution
6. [5] A1 for a 3rd correct solution with no extra solutions in the range. All solutions must be from correct working.