Plz must show pick brainiest solve, finding all solutions in [0,2pi) tan^2(x)+4=2sec^2(x)+tan(x)

Replace sec^2 with 1+tan^2 and solve the resulting quadratic.

.. tan(x)^2 +4 = 2(1 +tan(x)^2) +tan(x)
.. 0 = tan(x)^2 +tan(x) -2
.. (tan(x) -1)*(tan(x) +2) = 0

From the zero-product rule
.. tan(x) -1 = 0 . . . . . has solutions x = {π/4, 5π/4}
.. tan(x) +2 = 0 . . . . has solutions x = {arctan(-2)+π, arctan(-2) +2π}

Ibelieve the answer is c i worked it out three times but if my answer is wrong someone correct me