2sin

2 x + 6sin 2x = 7 (1 + cos 2x)

2sin (2x) + 6sin (2x) = 7 (1+cos (2x))

2sin (2x) + 6 sin (2x) = 7+7cos (2x)

8sin (2x) = 7sin²x+7cos²x + 7cos²x - 7sin²x

8sin (2x) = 14cos²x

16 (sinx) * cos (x) - 14cos²x=0

2cos (x) (8sin (x) - 7cos (x)) = 0

cos (x) = 0

x=π/2 + πn, n ∈ Z

8sin (x) - 7cos (x) = 0

8tg (x) - 7=0

tg (x) = 7/8

x=arctg (7/8) + πn, n ∈ Z