To solve the equation:

(sin3x + sinx) / cosx = 0

First, rewrite it as:

sin3x + sinx = 0

Now, we can use the sum-to-product trigonometric identity to simplify the equation:

2sin(2x)cos(x) = 0

Now, we have two possibilities for the equation to be true:

1) sin(2x) = 0
This implies that 2x = nπ where n is an integer.
Therefore, x = nπ/2

2) cos(x) = 0
This implies that x = (2n + 1)π/2 for n being an integer.

Therefore, the solutions for the given equation are:
x = nπ/2 or x = (2n + 1)π/2 where n is an integer.