tan(2theta +15)=1

The tangent(A) is = 1 at  45 degrees, 225 degrees, 405 degrees and 585 degrees

So, let A = 2Θ + 15

And setting 2Θ + 15  equal to the above values, we have

2Θ + 15 = 45          and solving for Θ we have Θ = 15 degrees

2Θ + 15 = 225         Θ = 105 degrees

2Θ + 15 = 405         Θ = 195  degrees

2Θ + 15 = 585         Θ = 285 degrees

And those are all the values that make the equation true for    0 ≤ Θ ≤ 360

You can see the graph of the solutions here.....https://www.desmos.com/calculator/xliaolg9le