ANSWER
[tex]\theta = \frac{\pi}{2} ,\frac{3\pi}{2},\frac{\pi}{4} , \frac{5\pi}{4} [/tex]
EXPLANATION
We want to solve the equation;
[tex] \cos( \theta) - \tan( \theta) \cos( \theta) = 0[/tex]
We factor to get:
[tex] \cos\theta(1 - \tan\theta) = 0[/tex]
Either
[tex]\cos\theta = 0[/tex]
Or
[tex]1 - \tan \theta = 0[/tex]
For
[tex]\cos\theta = 0[/tex]
We gave
[tex] \theta = \frac{\pi}{2} ,\frac{3\pi}{2}[/tex]
When
[tex]\tan \theta = 1[/tex]
Then,
[tex] \theta = \frac{\pi}{4} , \frac{5\pi}{4} [/tex]
Therefore the solution on the interval
[tex]0 \leqslant \theta \: \leqslant 2\pi[/tex]
is
[tex]\theta = \frac{\pi}{2} ,\frac{3\pi}{2},\frac{\pi}{4} , \frac{5\pi}{4} [/tex]
