To solve this equation, we first need to isolate the trigonometric function. We can do this by multiplying both sides by the trigonometric function's reciprocal, which in this case is -1/7.

(7/(tg(2x+π/8)) = -7)

(-1/7 7/(tg(2x+π/8)) = -1/7 -7)

(-1/tg(2x+π/8) = 1)

Now we can find the value of the tangent function by taking the arctangent of both sides:

(tg(2x+π/8) = -1)

((2x+π/8) = arctan(-1))

We know that the arctangent of -1 is -π/4, so:

(2x+π/8 = -π/4)

Now we can solve for x:

(2x = -π/4 - π/8)

(2x = -3π/8)

(x = -3π/16)

Therefore, the solution to the equation is (x = -3π/16).