Incorporate the use of the double angle formulas identities and other identities to solve for the following on $\displaystyle 0 \leq \theta \leq 360$

$\displaystyle tanx = sin2x$

My Attempt:

$\displaystyle \frac{sinx}{cosx} = 2sinxcosx$

$\displaystyle sinx = 2sinx$

$\displaystyle sinx - 2sinx = 0$

$\displaystyle -sinx = 0$

$\displaystyle x =$ 0 and 180 and 360

Textbook Answers:

0 and 45 and 135 and 180 and 225 and 315 and 360

What am I doing wrong?