Question: How can I get Maple to solve the following trigonometric equation

Essentially I have this trigonometric equation and I want to solve (get the roots of) it within the range -Pi..Pi:

v := a+b*cos(t)-c*(d*(1-(a+b*cos(t))^2-d^2*sin(t)^2)^(1/2)+e*sin(t)) = 0;
v1 := t > -Pi;
v2 := t < Pi;

Where t is the variable and a..e are constants.  At the moment I am trying the following:                  
solve({v, v1,v2}, t, allsolutions, explicit);

My problem is that Maple tries to solve this - I get Evaluating in the bottom left corner of the window - but never seems to return with a solution even after using 52,000s and 5GB of memory: I am using a late model macbook.

Can anyone see a way of re-framing this equation so that Maple can return an answer?

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