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If 2tan^2x-5secx=1 is satisfied by exact...

If `2tan^2x-5secx=1` is satisfied by exactly seven distinct values of `x in [0,((2n+1)pi)/2],n in N ,` then the greatest value of `n` is________.

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The correct Answer is:
7
Here `(2 sec x +1) (sec x - 3)=0` which gives two values of `theta` in each of `[0, 2pi], (2pi, 4pi], (4pi, 6pi]` and one value in `(6pi, 6pi +(3pi)/2)`.
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