Question 957305
<pre>
The formula to use is 

{{{tan(alpha+beta)}}}{{{""=""}}}{{{(tan(alpha)+tan(beta))/(1-tan(alpha)tan(beta))}}}

{{{tan(3pi/4+theta)}}} when {{{tan(theta)}}}{{{""=""}}}{{{1/2}}}

We substitute 

{{{alpha}}}{{{""=""}}}{{{3pi/4}}}

and so we substitute

{{{tan(3pi/4)}}}{{{""=""}}}{{{-1}}}

and we are given:

{{{tan(theta)}}}{{{""=""}}}{{{1/2}}}

Substituting in

{{{tan(alpha+beta)}}}{{{""=""}}}{{{(tan(alpha)+tan(beta))/(1-tan(alpha)tan(beta))}}}

{{{tan(3pi/4+theta)}}}{{{""=""}}}{{{(tan(3pi/4)+tan(theta))/(1-tan(3pi/4)tan(theta))}}}

{{{tan(3pi/4+theta)}}}{{{""=""}}}{{{(-1+1/2))/(1-(-1)(1/2))}}}

{{{tan(3pi/4+theta)}}}{{{""=""}}}{{{(-1/2))/(1+1/2)}}}

{{{tan(3pi/4+theta)}}}{{{""=""}}}{{{(-1/2))/(2/2+1/2)}}}

{{{tan(3pi/4+theta)}}}{{{""=""}}}{{{(-1/2))/(3/2)}}}

{{{tan(3pi/4+theta)}}}{{{""=""}}}{{{(-1/2))*(2/3)}}}

{{{tan(3pi/4+theta)}}}{{{""=""}}}{{{-1/3}}}

Edwin</pre>