so we have tan(165<sup>o</sup>)
=tan(135<sup>o</sup> + 30<sup>o</sup>)
tan(a + b) = (tan(a) + tan(b))/(1 - tan(a)tan(b))
=(tan(135<sup>o</sup>) + tan(30<sup>o</sup>)) / (1 - tan(135<sup>o</sup>)tan(30<sup>o</sup>))
tan(135<sup>o</sup>) = -1
tan(30<sup>o</sup>) = 3<sup>1/2</sup> / 3
=(-1 + 3<sup>1/2</sup>/3)/(1 - (-1)(3<sup>1/2</sup>/3))
=(-1 + 3<sup>1/2</sup>/3)/(1 + 3<sup>1/2</sup>/3)
=(-3 + 3<sup>1/2</sup>)/(3 + 3<sup>1/2</sup>)
=(-3 + 3<sup>1/2</sup>)(3 - 3<sup>1/2</sup>) / (3 + 3<sup>1/2</sup>)(3 - 3<sup>1/2</sup>)
= 3<sup>1/2</sup> - 2