To solve this equation, we can first simplify by factoring out an i from the second term:

Tgx + 2i * sinx = 0

Now, we can divide both sides by 2i:

Tgx = -2i * sinx

Next, we can divide both sides by sinx to isolate Tg:

Tg = -2i * sinx / sinx
Tg = -2i

Therefore, the solution to the equation is Tg = -2i.