As a general rule of thumb, initial 'th' is voiced in function words (the, then, there, those, that, this, though) and unvoiced in other words (thistle, thumb, third, theory, thorn, thing).
Initial 'thr' (through) and 'thw' (thwart) are always unvoiced.
I don't know the reason for this.
To make /θ/, place the tip of your tongue between your upper and lower teeth.
Push air out of your mouth between your tongue and your teeth.
You should feel some friction (resistance).
Do not vibrate your vocal cords.
As in the other cases in which consonants are arranged in pairs (see table 2), /θ/ and /ð/ share manner and place of articulation and differ in voicing (/θ/ is voiceless and /ð/ is voiced).
This means that the only difference between them is that /ð/ is produced with vocal fold vibration and /θ/ without.