I have the following equation

phi = -arctan(sin(2*theta)*(cos(beta)-1)/(cos(beta)*cos(2*theta)-cos(2*theta)-cos(beta)-1))+theta;

In the denominator I wish to collect the two cos(2*theta) terms  into a single term, as in

Is there a straighforward way of doing it?

i recall having asked this question before and having received answers which unfortunately I cannot locate.

I wish to generate a sequence like
    a[1], b[1], a[2], b[2], a[3], b[3]

The following does not work for the obvious reason:

    seq(a[i], b[i], i=1..3);

What is the right way?

The equation tan(y) = 2*tan(x) defines y implicitly as a function of x.  Well, perphas "defines" is too strong a word, since there are multiple solutions for y.  However, if I am not mistaken, there exists a unique continuous solution y(x) that goes through the origin, that is, y(0)=0, and is defined for all x.

Question 1: How do we plot the graph of y(x)?

I have a roundabout solution as follows.  Differentiate the equation tan(y(x)) = 2*tan(x) with respect to x and arrive at a first order differential equation in y(x).  Solve the differential equation with the initial condition y(0)=0.  Surprisingly, Maple obtains an explicit solution:

which we can plot:

plot(rhs(%), x=0..2*Pi);

Question 2: Is there a neat way of getting that solution with algebra only, without appealing to differential equations?

In Maple 11 we have:

> A := <a,b,c>:
> a := 1:  b := 2: c := 3:
> convert(A, list);
                                   [1, 2, 3]

In Maple 2015 we have:

> A := <a,b,c>:
> a := 1:  b := 2: c := 3:
> convert(A, list);
                                   [a, b, c]

Is that change really intended?