[SalesForce] How to pass URL Parameters in an apex test class

I have a Visualforce which has a custom controller with the following code (snippet). As you will see it takes the value from 3 text boxes on the page, does some brief validation before opening a new page:

Page 1 Controller

public PageReference openSheet(){  
    if (!strday.isNumeric()){
        ApexPages.addmessage(new ApexPages.message(ApexPages.severity.WARNING,'Pleaseenter a correct day value.'));
        return null;
    }
    if (!strmonth.isNumeric()){
        ApexPages.addmessage(new ApexPages.message(ApexPages.severity.WARNING,'Please enter a correct month value.'));
        return null;
    }
    if (!stryear.isNumeric()){
        ApexPages.addmessage(new ApexPages.message(ApexPages.severity.WARNING,'Please enter a correct year value.'));
        return null;
    }

    PageReference newPage = page.crew_sheet;
    strday.leftPad(2,'0');
    strmonth.leftPad(2,'0');
    newPage.getParameters().put('day', strday);
    newPage.getParameters().put('month', strmonth);
    newPage.getParameters().put('year', stryear);
    newPage.setRedirect(true);
    return newPage;     

}

The Visualforce page that opens also has a custom controller and it uses the following code (snippet):

Page 2 Controller

public with sharing class CrewSheet {

Public String day;
Public String month;
Public String year;
Public Datetime specificDate;

functionalY fy = new functionalYUtilities ();

Public List<Object__c> listAlpha1{get;set;}
Set<String> gwRounds = new Set<String>();
Public List<WorkOrder> listAlpha1Results{get;set;}

Public List<Object__c> listAlpha2{get;set;}
Set<String> pcRounds = new Set<String>();
Public List<WorkOrder> listAlpha2Results{get;set;}

Public List<Object__c> listAlpha3{get;set;}
Set<String> gbRounds = new Set<String>();
Public List<WorkOrder> listAlpha3Results{get;set;}

Public List<Object__c> listAlpha4{get;set;}
Set<String> rRounds = new Set<String>();
Public List<WorkOrder> listAlpha4Results{get;set;}

Public CrewSheet(){
    //get the parameters from the page
    day = apexpages.currentPage().getParameters().get('day');
    month = apexpages.currentPage().getParameters().get('month');
    year = apexpages.currentPage().getParameters().get('year');
    //the following if statements were added in as the test class isn't passing the parameters
    Datetime missingdate = system.now();
    if(day == ''){
        day = string.valueof(missingdate.day());
    }
    if(month == ''){
        month = string.valueof(missingdate.month());
    }
    if(year == ''){
        year = string.valueof(missingdate.year());
    }
    String specificDate = day + '/' + month + '/' + year + ' 09:00';
    Datetime specificDateformatted = datetime.parse(specificDate);
    String nextDayText = specificDateformatted.format('EEEE');

    // At this point we use the dates/strings in queries ultimately displayed on the vf page...i've cut them out for make it easier to read.
}

}

I have been trying to write a test class for this, whilst I am a beginner I was able to find a lot of examples on line and I came up with the following. Unfortunately it doesn't work, the apex log always reports "invalid date time null/null/null 09:00". I did expect this as the parameters are obviously converted to datetime from strings etc but I thought passing the parameters would work. My test sample

Test Class

@isTest
public class testCrewSheet {

@isTest static void testCrewSheet(){

    String day;
    String month;
    String year;

    //previous test attempt - same end result:
    //Test.setCurrentPageReference(new PageReference('Page.crew_sheet'));
    //apexPages.currentPage().getParameters().put('25', day);
    //apexPages.currentPage().getParameters().put('04', month);
    //apexPages.currentPage().getParameters().put('2017', year);


    PageReference pageRef = Page.Crew_Sheet;
    pageRef.getParameters().put('25',day);
    pageRef.getParameters().put('04',month);
    pageRef.getParameters().put('2017',year);
    CrewSheet cs = new CrewSheet(); 
    test.setCurrentPageReference(pageRef);
    }
}

So to summarise, why aren't the parameters being passed in the test apex class?

Thanks – I am currently only achieving 21% of my code coverage so I havea bit of a way to go 🙁